It regenerated prior to the molting that led to the third head coming out; page 16 of last chapter shows its just-regenerated tail up in the air, dripping with typical regeneration-goo, while it's still a two-headed wyvern; then page 17 has Gaine looking back at the cut-off tail and say, "I'm sure I cut off its tail earlier..." right before he gets swatted, and then it evolves and molts and becomes the three-headed variety on the last page.
Yeah, but then at the end of the chap it's made clear that the head growth is thought to be molting, and from the story beat it seems clear that the tail is supposed to be as well, rather than the author just introducing two separate types of regeneration for a creature within one page of each other. I assume the author wants us to think that similarly to how an animal doesn't molt its skin all at once instantaneously (a snake has to pull its molt off slowly from front to back), the dragon molted its tail before the head, so even when it was just two headed, it was in the process of molting.
But also, I just wouldn't think about it too much. Aside from the extra skin, there's the fact that there's no reason for the tail to need molting in the first place, because the purpose of molting is shedding a hard surface to let a squishy inner surface have area to grow before hardening again, and a severed limb has no limiting scales like that. Some molting animals like crabs can regrow limbs, but it's in spite of molting hindering it, not because of it.