As said all too often by the devs, ZOI is NOT zone of control.
From DiplomaticModifiers,xml, this is how the AI reacts if you do the same.
<DiplomaticModifier>
<UniqueID>StarbaseInZOCWithoutOpenBorders</UniqueID>
<RelationEffect>-2</RelationEffect>
<UniqueID>ShipInZOCWithoutOpenBorders</UniqueID>
<RelationEffect>-1</RelationEffect>
<UniqueID>ColonizedWithinZOC</UniqueID>
<RelationEffect>-3</RelationEffect>
ZOC is I believe 5 hexes from any of your colonies. Otherwise, ZOI is the "cold war" or "proxy war" in deep space. And I'm quite sure that the AI is not sending constructor ships for the hell of it. The AI knows where they are (it has to scout, but has no FOW on higher difficulties), and are mining the closest ones available. If in your ZOI, you had plenty of chance to mine them yourselves.
Trade for their starbases, or go to war with them and nukem.