The Russian side arrive in south Wales in disarray after a run of just one win from their past nine games and with manager Viktor Goncharenko preparing for just his second match in charge.
Kuban sit bottom of Europa League Group A, while Swansea are top of the pile after wins over Valencia and St Gallen.
But Cisse has extensive Premier League experience having played for Liverpool, Sunderland and QPR, and hopes it can pay off and reignite Kuban's hopes of a place in the knockout stages.
"This is a crucial game for us," said the Frenchman. "The third game ends the first phase of the group stage, we have no points and if we want to go further in the competition we have to start getting points.
"I know the English league very well, it is an advantage for me and I will try to talk to my team-mates and give them some tips I know about Swansea.
"They play a very different type of football from the Russian league and we will need to adapt quickly as soon as the game starts. If we give them time to start playing their football we will be in trouble.
"I know this only too well having been beaten 5-0 by them when I was at QPR, but if we play good football we can cause them problems."
The 32-year-old, who is also Lord of the Manor of Frodsham in Cheshire, knows it may take time for Goncharenko to settle into his new job, but has been pleased with how the Belarusian has settled in.
"Every coach is different, when he was appointed he called me to ask what we had to work on," said Cisse.
"At the moment we have just started together so we are trying to adapt to each other.
"But I think there is a good connection between the coach and the players and I think we will do really good things tomorrow and you may be surprised as we can play some good football."