I noticed that when my controlled space is over another empire's system, this empire can colonize any free system within my territory, is this intended?

I think if you’re at peace or in an alliance with the other empire 

They definitely cannot colonize in your territory if you’re at war or in a cold war as your territory would be considered hostile space.

well it's a bug then, because i was definetly in a cold war with entire map. have you encountered it?

Nope 

no, no laws unfortunately. the thing is i had this Riftborn system near my borders and a few empty systems inside my space. when my influence was high enough to peacefully steal their system i noticed that riftborn colonies started to pop up on free systems inside my territory, same happens with Vaulters and Lumeris

nah, haven't thought about screenshots when that happened. currently waiting for a patch, if it happens again, then i'll be sure to share a save