I've noticed that if you terraform a planet in a system which has a minor race already in it, the newly terraformed planet never has any kind of population growth, particularly if the minor race then join your empire.

it takes some time until the minor gets ready to colonize the newly-terraformed planet. But because it helped to speed up the process you get rewarded in doing so by a slight increase in diplomatic popularity.

Hi again Mal, yeah I tried it again, it took maybe 40 or 50 turns but you're right, the population did start moving to the new planet. I guess I just wasn't being patient enough before I posted.

sure. Once you got the Minor under your control, you need to colonize the rest of the planets with a colony ship but as long as the minor is free he'll eventually do that by himself. Some race characteristics play a role in here, like tech grade (a very underdeveloped "middle age"-minor probably has difficulties to achieve something like space travel but here it is assumed that other races (mostly you as their helping hand so to speak) send over civilian freighters to do the job over time.

I can't determine if the minor's relationship with you increases gradually while you're terraforming their planets - or if it remains unchanged until, eventually, the minor is ready to expand to another planet within their system and suddenly "realizes" that you've helped them.

it's a bit of luck and chance if the relationship increases or not. Usually it does. Just save the game at the turn before terraforming in the minor's system is complete and have a look at the barometer. Reload if nothing happens. You will eventually see a sudden increase. It's independent of the minor's continuous efforts to colonize the rest of the planetary system.