Just to clarify as another answer stated, a full vampire has to bite to cause this, not a vampire spawn?

You may also want to add what T.J.L. put in their comment in that this is the RAW of how it works, but a DM may have another mechanic that they are using. If they're asking about 'their pc at their table', the only person who can answer is that their DM.

It's also a bit unclear as to what "fed on" means from OP. It could be the bite attack, in which case your opening line isn't right.

@J.Wagner correct only a true vampire can create another of it's kind.

@NautArch The way it happened was not the main question though, I just wanted to know how Vampirism worked in RAW no matter how the RP went.

@J.Wagner That's true, but if you're looking for community guidance, the more information we have about your exact issue, the more we can guide answers to help.

RAW, it's extremely unlikely a player will ever turn into a vampire. Unless they have full HP and only ever take bite damage in a fight, it's very likely they'll die-die long before they die from reaching 0 max health.

Depending on which mythos you are using Vampirism can be possession as well ala Angel/Buffy and others (which makes making them an NPC fits the best imho). Bryan Lumley's Necroscope series makes it a parasite, so you could go several ways with it without really breaking anything.

The first sentence is incorrect. The bite attack has 2 damaging components: piercing and necrotic. Piercing damage is "puncturing and impaling attacks, including spears and monsters' bites". Necrotic damage is defined as being "...dealt by certain undead..." and it " ... withers matter and even the soul". THIS is the vampire's feeding. So yes, simply being fed upon by a vampire WILL transform you into a spawn assuming bite damage is healed.

@aaron9eee No, you need a bit more than "simply" being fed upon. These additional requirements are right there in the rules Bruno linked to and quoted.

"Vampire spawn become free-willed when their creator dies." - does 'free will' mean they transform into true-vampires in that moment? Or do we have three kinds of vampires: vampire spawns controlled, vampire spawns freewilled and true vampires?

@quetzalcoatl as the text does'n say anything about them transforming into true vampires, i assume they stay a spawn.

@aaron9eee the necrotic dmg thematically is the blood sucking, but you would also need to die (not be knocked unconscious) by the health reduction effect and then be buried to transform

@aaron9eee Again, for best results, read the actual rules. There are two important conditions that need to be fulfilled. 1) The victim must be killed specifically by the effect of the necrotic damage reducing their hit point maximum to 0. As you pointed out, the bite attack also does piercing damage, meaning the victim may end up dying simply because their current hit points ran out and (if applicable) they failed their death saving rolls (and the bite attacks will help those rolls fail). Or they might just not be bitten enough to die at all. Or they might get killed by some other cause.

2) If condition 1 is met, then the victim must be buried in the ground. If they're resurrected: no vampire spawn. Eaten: no vampire spawn. Disintegrated: no vampire spawn. Buried in a pile of laundry: no vampire spawn. Left out to rot to nothingness: no vampire spawn. Frozen in carbonite and hung on a wall: no vampire spawn. Although, arguably, that last example, depending on how well carbonite preserves, when combined with the inexorable march of time, may eventually result in the victim being buried and becoming a vampire spawn frozen in carbonite.