I move Irresistible Faefolk to Star Spring, I react to the trigger of Irresistible Faefolk with an Ambush unit. I use the Star Spring to send back Irresistible Faefolk to base. Can I drag a unit from my opponent with Irresistible?

Yes, you can move an enemy unit using Irresistible Faefolk’s ability in this scenario.

The Ruling

When Irresistible Faefolk is moved back to your base before its triggered ability resolves, the ability still resolves successfully. Because the ability references "that battlefield" based on the location where it moved to trigger, that reference is locked in at the time the trigger condition is fulfilled. Moving the unit before resolution does not invalidate the ability's target location.

Sequence of Events

1. Move: You move Irresistible Faefolk to Star Spring. This triggers its ability: "When I move to a battlefield, you may move an enemy unit to that battlefield."
2. Chain State: The trigger is placed on the chain.
3. Reaction: You play an Ambush unit to Star Spring.
4. Triggered Ability: Playing the Ambush unit triggers Star Spring’s ability: "The first time a player plays a non-token unit here each turn, they may move another unit they control here to its base."
5. Chain State: The chain now contains (from bottom to top): [Irresistible Faefolk Trigger] -> [Star Spring Trigger].
6. Resolution (LIFO):
   • Star Spring Trigger resolves: You move Irresistible Faefolk from Star Spring to your base.
   • Irresistible Faefolk Trigger resolves: The ability successfully resolves, allowing you to move an enemy unit to the battlefield where Irresistible Faefolk originally arrived.

Reasoning

While some abilities using the word "here" require a source to be present upon resolution per Rule 359.3.f.2, Irresistible Faefolk specifies "that battlefield." According to Rule 359.3.f.3, information referenced from the trigger condition (such as "that battlefield") is checked when the trigger condition is fulfilled. Consequently, the ability retains the data regarding the initial location, and the movement of the source unit does not cause the ability to fail.

Note: I could not fully verify this ruling against the retrieved rules.