“Always” alignment does not actually mean always
Always: The creature is born with the indicated alignment. The creature may have a hereditary predisposition to the alignment or come from a plane that predetermines it. It is possible for individuals to change alignment, but such individuals are either unique or rare exceptions.
Note that creatures with acquired templates do not experience “birth,” so the first line does not apply. Becoming a vampire “always” changes one’s alignment, but in rare cases (perhaps as in the case of your NPC), that can be subverted.
And even in the cases of Evil vampires, they can be reformed. There’s even an explicit spell for doing that (santify the wicked from Book of Exalted Deeds), though I strongly encourage you to completely ignore it as it’s very poorly designed (like most of that book), and has some extremely unfortunate implications (if you ignore the fact that the books says it’s good, and read it, it sounds like a pretty awful, evil thing to do to a person).
Thus, yes, you can have a non-Evil vampire. Redeeming Evil creatures is not just a Good act, it is the quintessential Good act.
That said, no character is ever required to always act for the maximum Good; it is not an Evil act to choose to not perform a possible Good action.
That said, assault and murder are pretty much definitively Evil...
Evil Alignment is consistently not an acceptable reason to attack someone
Attacking someone without specific cause is assault, which is Evil and in most jurisdictions illegal. Continuing that assault until the target dies is murder, which is definitely Evil and illegal most everywhere.
A paladin who attacks someone purely on the basis of pinging for detect evil should, under the rules, fall on the spot, for willingly commiting an Evil act.1
This is described in multiple rulebooks. It’s one of the few things about alignment that actually is somewhat consistent.
Alignment is not a detailed or consistent system
Alignment is described in different ways in different books, and the definitions are vague, ambiguous, and conflicting. The system is a historical artifact of D&D’s roots: it is designed for a simplistic, hack-and-slash dungeon crawl, where the players are Good because they are the players, the goblins, orcs, and vampires are Evil because they’re the enemies, and no one ever thinks too hard about that. Unfortunately, D&D has evolved but alignment hasn’t evolved with it; though people play far more serious and varied games than a straight dungeon crawl, alignment is still the same nine boxes. Don’t expect much from it; I actually strongly encourage you to ignore it. Outside of those simple dungeon crawls, it causes more headaches and arguments than it will ever be worth.
1 I cannot more strongly recommend against the actual falling rules, however. Instead of stripping the paladin of class features (boring, interrupts the story, punishes the player), I strongly recommend switching the character to the appropriate alternate alignment variant paladin, so he keeps his powers they just become “dark” (or chaotic if that’s the way he falls).