I don't think this is a Plus bug. I remember this problem happening before Plus existed, and in the thread you linked there are other people also saying it happens in the vanilla version (at least 1.24--I would check if the bug was introduced in 1.24, but I don't have access to a copy of 1.23 at the moment. I don't know where my old JJ2 discs are, so all I have is the GoG version.)

EDIT: Someone in the other thread mentioned the jingles do work in full-screen. I can confirm that fixes the issue, but it might still be worth fixing it for windowed mode in Plus at some point.