Same Safari Windows Appear in All Spaces/Desktops

This problem appeared for me not long using MacOS 10.13.3 and continues with the recent update to 10.13.4.

I use multiple Spaces (aka Desktops.) (e.g. I may open Apple Mail in one Space, then move to another space and open Apple Calendar.)

Recently one day, I found that when I have Safari open, the Safari window APPEARS IN EVERY SPACE. I found it covered any other app window I had open in any of the Spaces. Something just changed slightly today, where the Safari window covers over any app, but only for a moment, than steps backward behind whatever other app window is open in that Space. But, the main problem remains: that same Safari window will appear in every Space. This problem does not appear using any other app: it's only with Safari.

I found someone posted the same problem late last year, with no fix posted that worked. (There was one fix offered, which is to use Terminal command to "killall Dock". I tried that and it did not fix the problem.) I've browsed and searched, but cannot find current posting about this, so it might be a more obscure problem.

Any ideas? Can I fix this, and how? Or do I have to wait for Apple to clean up the OS and/or Safari?