This is a known problem although it is usually seen the other way round in that the originating site upvotes too much.
Personally I think the solution is to just stop migrations, the convenience to the OP of migrating questions is far outweighed by the problems caused.
Off topic questions should just be closed as such and the OP should be advised that $elsewhere may be more appropriate (based on voting like it is now) but to search first. This is pretty much what I do unless someone from $elsewhere asks for something to be migrated.
It's not like it's difficult for an OP to copy+paste their question to another site if they see fit to do so.
