I disagree with you on both the intent and the actual wording of the rules.
Every benefit of a long rest happens at the end. Since the rules do not prescribe an ordering, I take the following events to be simultaneous:
a) Each PC "regains all lost hit points" (from the Long Rest rules).
b) The PC's hit point maximum stops being reduced (from the Life Drain ability).
That's pretty clear. You lost 8 hit points to the specter's attack; now you regain those lost hit points. You can't regain hit points above your max, but your max is now back to 15, so you're fine. That's RAW, and I see no reason to believe it isn't also RAI.
That said, I would have no problem at all with a DM ruling as you did. It's a house rule, but it's a straightforward one, it doesn't imbalance anything, and life drain
should be nasty and scary.
All of this has raised a question I haven't seen answered in the FAQs yet (or I missed the details): A character with a 20 hp maximum and 5 points of damage (15/20) is hit by a lifedraining attack for 10 hp. Is the characters' hp total now 10/10? 5/10?
5/10.
All Life Drain effects reduce your max hit points "by an amount equal to the damage taken." So your 15 hit points get knocked down by 10 (to 5), and your 20 max hit points get knocked down by an equal amount (to 10).
Note that this means if you have necrotic resistance, or something else that reduces the damage, it will also reduce the Life Drain. At no point will you ever end up with your max hit points being reduced below your actual hit points.
