ok so i could be completely off the mark here, but this is my thoughts on why she said yes...
*throughout the series we know that they have to be careful about everything that they say or do as there could be several meanings behind the words that they say or actions, eg: katniss eating the berries (for love or rebellion?), haymitch saying 'remember who the enemy is (the other players or the capitol?), so we obvioulsy know that they are quite adept at doing this,
*when plutarch is showing the squad the hologram of the districts and the capitol and how the 'pods' have been laid out, finnick starts off by saying 'ladies and gentleman.....' and katniss finishes for him 'let the 76th hunger games begin because the hologram shows the layout of an arena, through katniss and fennicks eyes they and everyone else are once more 'pieces on a chessboard' playing another game, so wouldnt you say that Primm was also a 'piece' in the game aswell???
*while the victors have gathered to vote, comments are made about how they are the last remaining victors of the games, all the other victors are dead.
*remembering all this i believe that katniss say 'i vote yes for primm' she is saying that this is what she would do for primm, because in her mind primm was a gameplayer..........however would she make the same decision for herself, the mockingjay, the symbol of the rebellion and of the people??????
by haymitch then saying' i'm with the mockingjay', this reconfirms that he understands that this is not katniss' nor the mockingjays decision but something that she would do for primm only.