Hello RaveryS, On your Mac computer, go to Parallels Access -> Preferences -> Advanced -> Select : Lock the computer when working remotely and check!
There are different result at my different Macs, one of my iMac just dim light but not turn off the display. Another Mac is fine.
By the way, It cannot recognise the Mac correctly in my iPad, after I migrate to new Mac from old one (both old and new Mac are still using, and they have different home directory changed by myself at Terminal), that means I just can recognise one of that two Mac at the same time.