As a Terran In a 3 "colonizeable" planet star system I had the following happen:
The Planets:
- Size 8: Aquatic Influence Output: 5
- Size 12: Earthlike Influence Output: 11
- Size 13: Lush Influence Output: 12
The Yor populated the Size 8 and somehow captured both of the other planets through influence. At the time I tried to put up 2 culture star bases in order to stop my planets from defecting but no luck.
They did have 4 planets in medium proximity to my 3. However, my population on those planets were larger.
I don't think influence is working completely correctly.