"Guys, Vasya seems suspicious, I think he's Mafia. Execute Vasya."
A couple of minutes later.
"No, guys, Vasya is good, let's hang Petya instead. You can see 'MAFIA' written all over his face."
Okay, -1 Mafia team. We can add some more evidence to the accusations...
1) tighten the rules, applying them to such cases (I don't like this option).
2) let zombies not be able to win at all, in any situation (then another problem might arise, that they will help their old teammates).
3) complete puppet: either they don't write anything at all and are controlled by the Alchemist at night, and don't communicate with the Alchemist (but then you can allow communication in the Mafia chat), in short, they almost don't participate in the game, it all depends on the Alchemist.