The ability tracks the creature, but not its controller. If the creature changes controllers before its first controller's next untap step has come around, then it won't untap during its new controller's next untap step.

Guardian of Tazeem's landfall ability can target a creature that's already tapped. If the land that caused it to trigger was an Island, that creature won't untap during its controller's next untap step.

A landfall ability triggers whenever a land you control enters for any reason. It triggers whenever you play a land, as well as whenever a spell or ability puts a land onto the battlefield under your control.

A landfall ability doesn't trigger if a permanent already on the battlefield becomes a land.

Whenever a land you control enters, each landfall ability of the permanents you control will trigger. You can put them   on the stack in any order. The last ability you put on the stack will be the first one to resolve (As a result, you can have those abilities resolve in the order of your choosing.).