Undead is not the same as dead. In fact, just judging by the linguistics involved, it's kinda the opposite.

Also, of COURSE it's "convenient" that the tadpole just so happens to alter the nature of a vampire spawn in such a way that they become a functionally playable character in the game. This is what game designers do all the time. Sometimes, a particular bit of story or setting is SO important that you tailor the gameplay itself around that narrative element. But most of the time, you design the gameplay you want, and then come up with whatever story excuses you have to in order to fit that gameplay. If this is done very skillfully, it's invisible to the player, but often on big projects with a lot of moving parts, you just don't have the time to perfectly craft an airtight narrative justification for every little element in the game. Especially when 90% of the players literally won't care anyway.