Animation "pops back" to frame zero after leaving the animation controller state playing it?

I’m very frustrated with this problem, I’ve been struggling with it for many hours now. My animation controller states look like this:

FadeInMainMenu > FadeOutMainMenu > FadeInOptions

Fade in/out main menu are using the same animation - one playing in reverse using negative speed. When the controller transitions from the end of FadeOutMainMenu to the beginning of FadeInOptions, the main menu suddenly snaps back into visibility, as it was at the end of FadeIn and the beginning of FadeOut. Why does the animation for that object revert back to its first frame after the animation is done?

I don’t have the animation set to loop, and all my transitions are set to completely finish the current animation before starting the next (no overlap):

Has Exit Time = true
Exit Time = 1
Fixed Duration = true
Transition Durations = 0
Transition Offset = 0
Interruption Source = None

All my animation controller states are set to “Write Defaults = true”. I tried experimenting with various combinations of that setting on different animation states in the order, but nothing I tried helped.

So I changed my Exit Time from 1 to 0.999 and it works with out popping back.