Mana Vault reads, "At the end of your upkeep, if Mana Vault is tapped, it deals 1 damage to you." Unlike most artifact abilities, this one is played if Mana Vault is tapped but not if it's untapped. If Mana Vault is untapped when it's your turn to play abilities at end of upkeep, you don't play its ability. If you finish with the series and your opponent then plays an ability that taps Mana Vault, you don't back up and play its ability after all.