Matsatsatsanta overcame the challenge of a daunting trip to Tunisia, where they defeated Club Africain 4-2 on aggregate to advance to the Confederation Cup final for the first time in their 23-year existence.
Sibiya was visibly ecstatic at the team's achievement upon their return to OR Tambo International Airport on Tuesday, describing it as the biggest moment in United's history, before praising Tinkler for picking up right from where former coach Stuart Baxter left off.
"This to me is the single biggest moment, not only for the club but for the country as well, it's just overwhelming," said Sibiya.
"It is a milestone. It is something we will cherish for a long, long time. Stan [club CEO Matthews], you and I have been going down and up, down and up with this club... This is it!
"We have done an amazing job, and I want to congratulate Eric. Eric, you have come to this club and you have made things happen.
"It is very unusual for any new coach to come into a new club and just make things happen. You're an amazing, amazing man."
Sibiya also gave credit to skipper Dean Furman, Reneilwe Letsholonyane and "prodigal son" Morgan Gould, as he then called on 'Mzansi' to come out in numbers and get behind the team in blue for the second leg of the final at the Lucas Moripe Stadium in a month's time.
"Please go spread the word that this victory and the upcoming final is not for SuperSport, but for the country," he added.
"Tell everybody out there that we are bringing this trophy home, and we need your support. We must make that stadium blue.
"It must be a crowd that we've never seen supporting SuperSport before, so please spread the word and tell everyone that we mean business."