Kaya exiles temporary Lockdown, what happens? - eviltoast

Okay, so today I had a weird interaction. My opponent played a temporary lockdown. I exiled it later with my Kaya, Intangible Slayer.

This produces a 1/1 spirit token, that should theoretically exile itself. This did however not happen in Arena. Why is that?

Is it a bug or is there a rule that I don’t know?