How do encounter card vampires work in combat?
From 3rd edition rules reference:


  Vampire Encounters 
  
  Combat with a vampire can be initiated from
  Dracula’s “New Vampire” and “Reckless Vampire” encounter cards. The
  rules in this section apply only to vampire encounters; when the word
  “Dracula” is used, it is referring to the Dracula player. 
  
  † If a hunter either resolves a search action or is ambushed in a hideout or
  lair and an encounter card is revealed that reads, “fight this
  vampire,” a combat occurs. 
  
  † Combat against vampires uses the same
  rules as combat against Dracula with the following exceptions:
  
  
  “New Vampire” and “Reckless Vampire” encounter cards have their own health
  values. When one of these vampires suffers damage, it is tracked on
  the card using damage tokens. If a vampire has a number of damage
  tokens on its card equal to or greater than its health value, that
  vampire is defeated.
  When a vampire is defeated, its encounter card
  is discarded. If combat ends without the vampire being defeated, the
  damage it suffered remains on the card. 
  
  
  † If Dracula plays “Escape as
  Mist” or “Escape as Bat” before he has played a number of combat cards
  greater than the number of despair tokens on the time track, the card
  is canceled. 
  
  
  If Dracula resolves “Escape as Bat,” combat ends, but
  neither Dracula nor the vampire are moved from their current
  locations.
  


To summarise: combat is played out almost exactly the same, except fledgeling vampire tracks their own health and escape cards don't move it.

Also, if a combat ends and vampire wasn't defeated, it stays in location (retaining damage), and if revealed vampire reaches end of the Trail, it still can trigger its matured effect.