You're misunderstanding me. First of all here's a quote from the documentation of COMMON_DOMESTIC
COMMON_DOMESTIC Allows the creature to be brought with immigrants and when creating a new fortress, as long as the creature also includes at least one of the following tokens: PET, PACK_ANIMAL, WAGON_PULLER, MOUNT. In addition, the creature must be NATURAL rather than FANCIFUL
The common domestic tag on your caste causes 3 things to happen:
1) The creature becomes available on embark as a pet.
2) (stray) nameless unowned animal version of the creature will show up along with migrants.
3) named owned pet animal versions of the creature will show up along with migrants
This is all assuming the creature also doesn't have something like the [EVIL] tag and your race entity lacks the USE_EVIL_ANIMALS tag.
In none of these cases are they actual migrants. They are stray animals, or pets. They will not perform any labors (unless having CAN_LEARN changes that, I don't know), they will just mill around in meeting halls with the other animals and do nothing. In 40d, 3 was common, 2 was rare. In df2010, 2 is common and 3 is rare. Most animals now arrive (stray).
However, because the creature in question is a subcaste of your race, you will ALSO get migrants versions of them. These will have names, and they WILL perform labors, and they will show up with random labors enabled. If they don't have CAN_LEARN, or if they do but also have SLOW_LEARNER, I think you'll see the behavior of them arriving with job titles and labors enabled but without any skills(the slow learner tag has a very powerful effect).
The POP_RATIO tag is just a weighted birthrate, the default is 1. If you set the pop ratio of males to females as 1 and 10 respectively, it means 1 in every 10 dwarves will be male, the rest female.
The pop ratio you describe set the birthrate to something like 1 out of every 20000 dwarves born will be a 'slave caste,' the rest split evenly as normal male or normal female. This means any babies or immigrants have an extremely low (but not non-existant) chance to be created as 'slave caste.' Your anecdotal evidence also implies that it DOES affect how often the creatures will show up as COMMON_DOMESTIC pets or strays along with migrants, which is interesting and undocumented. At the same time, it has no effect whatsoever on the embark ability to buy the creature, you can purchase however many of them you want.
For my race, I wasn't intending to play as Gorlocks, I just made them playable to test them out a bit. I wanted to be dwarves and have access to gorlock slaves. So:
1) I made them COMMON_DOMESTIC so they would be available on embark and come as animals with migrant dwarves.
2) I made them MALE so they wouldn't breed in my fort, but would still contribute to the breeding population of the race as a whole in world-gen.
3)I made them not have CAN_LEARN, so they could be milked
4) I made them not have CAN_SPEAK, because I don't know what effect it would have (you say it prevents butchering, ok)
5) I was more interested in them being able to be milked/butchered than in them being able to perform labors, so I didn't mess around with the CAN_LEARN tag to see if it was possible.
While I was testing all of this by playing as Gorlocks, I did notice one inconsistency. (stray) gorlocks could be butchered and milked, but NOT put in cages. The game still considered them enough of the playable race that I couldn't put them in cages like a normal animal.