The scenes were understated but not unexpected. As those under his guidance savoured the moment with the supporters, Philippe Clement stayed out of the limelight and kept his sense of satisfaction at a job well done largely to himself.

A brief exchange with Steven Naismith followed in the seconds after the full-time whistle at Hampden. Clement applauded the fans in the main stand – and the directors that watched on from their vantage point at the rear of it – both before and after a venture onto the pitch. Clement would do the rounds with many of his own players and the Hearts side that had just been beaten, offering an outstretched hand in commiseration or a cuddle in celebration.

Connor Goldson was the first to be embraced by the manager. As Clement made his way around the park, the main man in the recent revival took a back seat while songs reverberated around the Rangers end. He encouraged Leon Balogun to go and join those players that were taking the acclaim from the crowd and then ushered Leon King and Ross McCausland to do likewise, despite them playing no part in it. That sense of unity, of collective responsibility and achievement, is underpinning Rangers' upturn in fortunes.

This was a win that was masterminded by Clement but that was earned by his players. It was they that he wished the adulation to fall on in those moments after two efforts from James Tavernier and one from Scott Wright had seen off Hearts. The game could have been out of sight before a second-half flurry of goals, each one clinical in their own right, and the margin could have been wider come the end of a one-sided affair.

READ MORE: Rangers 3-1 Hearts: Instant analysis as Tavernier earns cup final spot

There was no sense of ego or bombast from Clement, never any danger that he would get caught up in the occasion. It became evident in Clement’s first hour at Ibrox that such a style was not in his make-up. His unveiling press conference last month gave an insight into the man and the manager and his words and his actions have made as much of an impression on his players as they have his fans. As the mood in the dressing room has been lifted, the sense of excitement – one which should still be tempered – has started to steadily rise.

Asked in his post-match press conference about reaching his first final, he responded by saying that it was not his cup final but one for his players and the club. The achievement was ‘not about individual satisfaction’. Questions about Tavernier and Danilo were answered but caveated with the position that he was loathed to single out certain players on a day when there wasn’t a failure in his team.

He also spoke about the way in which the ‘several leaders’ within his squad have stepped up since he succeeded Michael Beale. As Clement fine-tunes the component parts, the machine is becoming a well-oiled one and this win follows league successes over the Jambos, Hibernian and Dundee.

The Belgian could take satisfaction from a job well done on Sunday but he is wise enough to know that nothing has been won. He is cognizant of where Rangers are as well as where they must get to. With each performance and result, there is a burgeoning belief that Clement is the man to take them there.

Those who are getting to know Clement that little bit better with each interaction would have been able to predict his mantra post-match as feet were kept firmly on the ground. That message will no doubt be reinforced at Auchenhowie this morning as attentions turn to the Europa League fixture with Sparta Prague on Thursday evening.

“I will never judge myself from the outside, I do it every day with myself - and I’m critical - because every day I will make mistakes in this job,” Clement said. “But I know the story we want to build, that it’s a good story and I see everybody stepping into that story, giving full concentration to do it. And then you get fine football at the end with results.

“We have to continue like that and not go into a mode of satisfaction. That is the big danger now. The players can be satisfied this evening and happy and enjoy that time with their family but [on Monday] I expect everybody to be focused again towards Prague.

“That is football. OK, we are in a final but if you are in a final, a semi-final or quarter-final, it doesn’t make a difference. In the end, it is about winning something. We are not there yet.”

Clement is a man for the detail and the marginal gains. The Premiership title race and domestic cup competitions are the big pictures, but any ambitions on those fronts are irrelevant if the basics are not done first and foremost.

The preparations for Prague were described as a ‘puzzle’ given that Balogun and Ridvan Yilmaz are ineligible for the Ibrox fixture. It was intriguing that Clement again made the point about him having no say in the make-up of the squad.

A group that has so often been understrength, that has so often underperformed, now has a character and quality about it. Over the course of the upcoming international break, Clement will seek further advancements across each of the four pillars that he has laid out and Rangers will rightly fancy their chances of heading into that domestic hiatus with two more wins under the belt given that a trip to Livingston follows the visit of Sparta.

Much of the work undertaken thus far has been done in the analysis rooms at Auchenhowie rather than on the pitch as Clement has been confined by the schedule and the depleted squad that he inherited. The trajectory has all been up and up and the controlled nature of their performance, the clinical nature of the result, at Hampden was another small but significant step in the right direction.

“Surprised? I didn’t have expectations about that so then you cannot be surprised,” Clement said when asked about the speed at which improvements are being found. “You need to get to know the players, need to get to know the staff, need to get to know everybody. I am still working on that because I don’t know all the players in every reaction they can have.

READ MORE: Philippe Clement's full Rangers press conference after Hearts win

“I only see the players now when they have success, you also need players who are good when you have a disappointment and how they react. It is also a very important thing in football. I am still in the observation period in that way. I think we see already after two weeks a lot of good football, a lot of chances, a team who is dominant. The things I want to see and that we work on every day really hard.”

Those efforts are paying off right now for Rangers but a support who have endured more than their fair share of disappointments and lived through too many false dawns should take the words of Clement to heart. Now is not the time to get ahead of themselves and to lose sight of the trials and tribulations that will follow, even if each challenge that is overcome offers hope that there could be light at the end of the tunnel.

The targets upon Clement’s appointment were clear to lay out but far from certain to be achieved. Boxes are being ticked game by game. If Rangers can end the year within sight of Celtic and with European progression and the Viaplay Cup secured, then supporters will have licence to dare to dream.

Clement will continue to take it one game and one win at a time. If the doors to the Trophy Room are opened next month, perhaps even he will start to get excited about what can be achieved at Ibrox.