Except it isn't conflation. It's interpretation. You view the effect as tertiary. I don't. I see it as part of the same effect that kills the victim.
That’s conflation. You’re combining multiple effects into one. The target dies is one effect. The target rises as a vampire spawn is another effect. They each have their own separate conditions.
The reason “the target rises as a vampire spawn” is a tertiary effect of the bite is that the bite has three primary effects:
1. The target takes piercing and necrotic damage.
2. The target’s hit point maximum is reduced by the amount of the necrotic damage (restores on a long rest).
3. The vampire regains a number of hit points equal to the reduction.
Effect 2 gives rise to a secondary effect: the target dies if effect 2 reduces its hit point maximum to 0.
Which further gives rise to a tertiary effect: the target rises the night following burial as a vampire spawn under the vampire’s control if (a) the target is a humanoid, (b) the target is slain by the secondary effect of effect 2, and (c) the target is then buried in the ground.
Also, I think it’s worth repeating that the duration stated for the reduction of the target’s hit point maximum caused by effect 2 (until the target finishes a long rest) applies only to the numerical reduction of the target's hit point maximum itself and not to effect 2 in general or its secondary and tertiary effects. By conflating all of these, particularly the stated duration of the reduction and the secondary effect, you get the odd result that the target remains dead as long as its hit point maximum is 0, when that isn't a stated effect of the bite.
Both views are valid views. At this point that's the main contention. We see both interpretations as valid. Your side seems to view your interpretation as the one true way.
I can get to something like your interpretation by regarding the duration of the "reduction" (until the target finishes a long rest) as applying to not only the action of the hit point maximum being made less, but also everything that follows from that action (i.e. death if hp max is reduced to 0, etc.), but I would also need to make what I feel are some grammatical errors to get there. I think there's been a reluctance on the part of the defenders of your interpretation in this thread to discuss what those errors are.
My goal isn't to invalidate your interpretation. You're welcome to it. IMO, it relies too much on extratextual beliefs about what's going on in the fiction, but that's really just a matter of taste.