Overflow damage on a single hit does not transfer.
Subsequent hits transfer from the component that was hit to the "hull component" - meaning they apply damage to armor first, if any remains.
We've been unclear in the past on the terms for the two health bars on the hull (I try to refer to them as armor and health), which is probably part of the confusion.
Each hit (projectile, explosion, gatling or carronade ray/pellet) deals its damage to a single location, in a lump. Transferred hits function exactly as if you actually hit, say, a hull hitbox instead of a balloon hitbox. None of the balloon/engine/gun multipliers are applied; multipliers for hull armor or health are applied according to the hull's current state.
Note that there is a slightly weird case where a single hit deals more damage than remaining hull armor. Currently, in this case, the base damage is multiplied by the armor modifiers, and any overflow of that modified value is applied directly to hull health.
Also, for the record: there was a data bug in the original release of 1.1.4 that caused the Flechette damage type (the one used by carronades and other balloon-killers) to deal slightly less than twice as much damage to armor as was intended. This has since been fixed.