What I've seen is this:
Windows v10.3.7 on a MS Surfacebook 2: I add a tag to a note. If I search for that tag, I probably won't see that note for what sometimes seems like 10 or 15 minutes. If I look at the web version of EN, I can see the note when I search for that tag. My Google Pixel Android phone seems to see the tag change very quickly as well. If I quit the Windows app, then re-launch, I can see the change in tags for the notes, even if I wait less than 1 minute to quit/relaunch.
My database isn't very big; just under 1100 notes in 2 notebooks. I use tags to separate notes in a way that makes sense to me.