A couple years ago, I was given two Baofeng HT radios. One of them had the same delayed receive issue. As you stated, it was rather annoying when someone was quick to key up. No idea why it worked that way.
Possibly something in the programming settings. Maybe something to do with squelch level settings or DCS or the squelch tail eliminator. I don't use those two radios anymore, but I'll charge them up and see if I can figure it out in some limited spare time. If I come across a valid cause, I'll post it here.
Doug
WRPG 593 / N9ULL