Matsatsantsa were welcomed to a mass celebration at OR Tambo International Airport on Tuesday, after walloping Club Africain in their second-leg semi-final in Tunis on Sunday evening.
United may have made club history when they qualified for their first ever cup final outside the borders of South Africa, but still have a huge task in facing defending champions TP Mazembe in the two-legged final next month.
Tinkler, who has experience of that particular stage when he was unable to steer Orlando Pirates past Tunisian side Etoile du Sahel in the 2015 final, is well aware that they cannot get carried away despite their historic achievement.
"The important thing is to be humble. Yes, it's a fantastic achievement to get to the final but, as the players know, we haven't won anything yet," said Tinkler.
"Obviously I've experienced and tasted what it's like to get all the way there [to the final] and lose, and we don't want that, we want to go all the way
"How do you do that? Remain focused, be humble, stay away from the press because they're always going to cause you more issues – they want more interviews – and we need to be humble and quiet.
"Yes, we feel really, really excellent inside, but the job's not done yet – that's the important thing [to remember]."
Having come in midway through the competition after taking over from Stuart Baxter and Kaitano Tembo in June, when SuperSport were already in the group stage, Tinkler gave credit to the players and the technical staff for their efforts and the foundation they laid.
"It's a moment of pride for everybody at the club and for myself, but the players and the technical team – Kaitano – must take all the praise," he added.
"I only came in right at the end, but they travelled the long road and the passion, desire and determination to go far in the competition – they've always had it.
"That made my job a lot easier, so I was just extremely proud of the performance we saw on Sunday night."