Evasion checks are required when you are in a space with a monster and attempt to perform a non-attack action.
In your example, lets say you start in the room with two monsters so you can have two actions this turn.
If you spend your first action attacking one of the monsters, you do not require an evade check against it. If you spend your second action attacking either of the monsters, again you do not require an evade check.
However, if you want to spend your second action searching/moving/doing anything but an attack action against either monster, you do need to do an evade check against both monsters (if you didn't kill the first during the attack action), since they are both still in the room.
On the other hand, if you spent your first action entering the room, and the second action attacking - then there is no reason to do an evade check since you are not doing any non-attack actions.
In most MoM scenarios, there are only ever a few monsters on the board, so this particular situation shouldn't come up too often, but yeah - multiple monsters in one room can spell bad things for the investigators!