>>   Seems like whenever `y-or-n-p' (or just `read-key') is waiting
>>   for a key, `message' should do nothing.  Either it should echo
>>   its message after the key is read or (maybe better) it should
>>   do nothing at all.  As it stands now, this seems like a basic
>>   UI problem, not just a minor annoyance.
>
> I tried this here with emacs 25:
>
> (progn
>   (man "X")
>   (y-or-n-p "-->"))

Here is the patch that fixes this (required changes from bug#38076):