I just tested this myself in NewUX and I couldn't replicate this issue. I tried searching on a parent level that I didn't have access to and it wouldn't show up. I also tried searching on an child level - selective access is working well. My suggestion would be to double check the User security for the parent level to make sure they don't have access because it appears as if they do.
If you can provide some more details about how the selective access is set up for P1-P3 for this user I'd love to help you figure this out. Sorry, not the best answer but I guess I need to know more about your configuration to identify what's going on.