An effect that does not require concentration can be carried across because it is affixed to the target of the spell. A spell that requires concentration cannot, unless the caster and the target cross the barrier at the same time (or the caster is the target.) A spell or spell effect cannot be maintained on a target on the other side of the boundary.
An easy way to think of it is that the boundary is, for the purpose of spell effects only, a vast distance and another plane of existence.