We have always played it that monsters that appear when gates from Mythos cards are played don't move with the icons. In a game tonight someone suggested that they should do, but we can't find anything in the rules to say so.

I think we'll always house rule it that they don't because it makes more sense to us, but pondering where it may otherwise say in the rules. Thanks.

I don't think it's spelled out in so many works, but if you follow the steps under Phase V: Mythos (p. 9) you'll see that resolving a monster surge or placing a new gate and monster come before "Move Monsters" so adhering to this order, you'll place the new monsters and then move them with all the other monsters already on the board.

Oh, and also following the Mythos phase order in the rules, additional monsters that appear due to the Mythos Card text ("picnickers release two monsters into the streets," etc.) DON'T move that turn because "Activate Mythos Ability" comes after "Move Monsters" in the order of operations.