I'm using the dynamic window manager of suckless (dwm). I noticed that firefox is able to send nice notifications when a download has finished. See the two figures

When I'm on a different tag, I get this kind of notification (inverted 1 tag) upon a finished download.

I'd like to use this kind of notification for my other uxterms. E.g. in case a long job has finished it should light up like above. At best, this would also work inside the GNU screen sessions that I'm using.
I'm not sure if this is a Xorg or a dwm feature. Any ideas?
EDIT: The answer of @scai is very much to the point, but lacks the full compatibility with GNU screen. In case anybody can still improve this, it'd be very much appreciated.