I just confirmed that they don't auto-improve in another civ's territory. What they were doing is trekking 16 sectors across the galaxy to get unclaimed 'roids, and the AI set set up some colonies and expanded borders during the whole frikkin' year it took them to get there.
This is on immense with abundant asteroids, so there were way more 'roids than the AI bothered to mine. Directing all my miners ended up being an epic micromanagement quest. I wouldn't mind some kind of tweak to keep miners within a certain distance of my borders, or to upgrade a nearby mine if the nearest unclaimed 'roid is too far away.
If I want them to travel all over hell and creation I can send them manually. I'd fire those miners and hire robots if the jerks weren't unionized...
(ha ha ha, I said roid)