The synthesist’s fused eidolon isn’t a separate creature, not really, not in game terms. It doesn’t have its own space, AC, saves, and so on. It doesn’t get targeted separately from the synthesist. Instead, it’s more like a buff effect that’s operating on the synthesist, albeit a strange one.
Which means not only does the fused eidolon not lose hp, it doesn’t even have hp to lose. It’s not a creature with hp. It’s a buff that grants temporary hp, and has the unusual condition that it ends when those temporary hp are lost.
The reason you see references to a creature, with stats, is because of the unusual way the bonuses of the fused eidolon buff are calculated—you stat out a non-fused eidolon creature, as normal for a summoner, and then you use that creature’s stats to determine the effect of your fused eidolon buff. But until the summoner gets split forms at 16th level, the non-fused eidolon creature never actually appears in the game world. The synthesist has no ability to summon it un-fused until then. The stats you create with it are hypothetical, an intermediate step in determining the effect of your fused eidolon buff.