I think the behavior is the same.
I’ve heard of this trouble with piz website. I got them before that. Maybe you can still get around it somehow.
https://www.kvraudio.com/forum/viewtopic.php?t=490010
The plugin caused a note off to be sent at the time of the overlapping notes note on. So reaper overdubbed two notes. Some theories went through my mind that this would not solve all problems, or maybe an unequal number of note ons and offs might result, etc, but maybe worth a try if you can get it.
I’m curious. Does the drum pad have the ability to hold two note offs? You can end both notes where you like, in other than overdub?