It varies for me, but generally I put them in when around .010 oversized.
If you go down to very small tools, depth of cut becomes and issue, especially if your inlays are not narrow. The wider they get, the deeper they have to go, because of the radius of the cue. With a wide inlay, sometimes I'll only have .010 on the outer wall of a pocket, even cutting .14 deep. Some advanced programming is needed if you want to clean up corners and such with a cutter than only goes .060.
Obviously, materials will dictate as well.... some materials you just can't get very thick, so you have to give yourself every advantage you can get, which means cutting inlays with the cue very close to finished size, or even at finished size.
I've put lots of inlays into finished cues as well, then cut them down flush (just barely cut through the finish) and refinish.
Inlay with the cue too far oversized, and you could risk losing edges if the cue moves.... Depending on the inlays, of course.