Interior soffits should be airtight before the drywall goes up
Soffits should not be like false ceilings, but rather they should be enclosed boxes hidden in your ceiling. Because they usually hide some sort of mechanical work (plumbing, wiring, ducting) they should be inside the conditioned envelope, not outside it.
How to do it: Seal the sides and top with OSB or drywall for soffits that hold ductwork, can lights, and exhaust fans.
In this video, Bill Hull of W.H. Hull Company shows a sealed soffit over a shower in a zero net energy home that his company has built.
—Video courtesy of Zero Net Energy Homes