Does successfully opening the vault end your movement due to drawing the item cards?
Yes, drawing a card for any reason ends your movement.

As you pointed out, the rules (page 5) make it clear that drawing a room tile with a card symbol does this:


  The first time you discover a room with a card symbol, you must end your move in that room and draw the appropriate card.


The rules for movement (page 4) clarify this further:


  Whenever a game effect makes you draw a card, you must STOP moving for the rest of your turn.


So any game effect which makes you draw cards (and if you're not cheating you should only be drawing cards based on 'game effects'!) ends your movement. This includes things such as successfully opening the puzzle box item, so try that at the end of your turn unless you really need the item!