There are 3 possible swaps during a cycle of the twins mechanics:
1) Boss swap: Tanks taunt the opposite twin after colors are recieved.
2) Minor swap: Shortly after the groups recieved their respective colors 3 players from each group (excluding tanks) are randomly chosen for changing colors (you see that by a circle beneath your feet). This players have to join the opposite group without running into each other - otherwise BOOM.
3) Major swap: Shortly after minor swap the twins are starting to pray (each in a half of the arena). The whole group has to run to the twin they just fought (so opposite color). If you are lucky, you don't have to move tho, that's why xynode is calling this phase "switch or stay". If you stay in the half with the twin matching your color - BOOM.
As soon as colors are removed by the explosion, tanks (not group!) run to their original boss (the one you started the fight at). Rinse and repeat.
Most important advice: Everybody should always run into the same direction during both swaps (usually clockwise, but counterclockwise is possible, if the whole team is doing so) instead of criss-cross - otherwise it's BOOM BOOM BOOM.
Rakkhat is another beast in MoL tho, don't think it will be as easy as the fight in IA.