yes this is perfectly normal.
When any application uses ASIO, Windows gives full control to that application.......removing sound card access to that application. The only way to get that application to play music or something else is to exit out that application (although I have seen that simply stopping playback (on that application ) also releases exclusive control)
This is by design.
For example:
When I play music in a software called MusicBee (which is configured to use ASIO), all other applications/software and even Windows itself cannot play anything.....like Windows' ding sounds etc do not come through. This behaviour is normal and is expected and also is mentioned in the ASIO driver's readme file (I am using Cambridge audio ASIO on my workstation)
BTW this has nothing to do with REW