I don't know, because neither "reversibility" nor "determinism" are precisely defined (this is not criticism of your comment in any way).

Here's one semi-reasonable interpretation of the two words for which reversibility would not imply determinism: Imagine a "process" (I, too, am being imprecise and calling this a "process" instead of a function) that takes as input an integer between 1 and 6 inclusive. Its output for the input n is a dice roll with a dice that is biased in favor of n, but is otherwise fair. Now, this is not a deterministic process, but if you are allowed to feed it the same input multiple times, you can probablistically reverse it.

Anyway, sorry for the tangent – your original point was the important one.