If their is a possessive adjective, then so is its. The the words function in the same way in your two sentences.*NOT A TEACHER* "Their" is a possessive adjective as: Their house is the biggest one on the street." "Its" is a pronoun indicating possession: Its beauty is breathtaking.
My point was simply that, no matter how we label them (and I am not a great labeller), we need to use the same label for 'their' and 'its' in your sentences.*NOT A TEACHER* They do have overlap in use and I agree they can both be classed as possessives. I'm not yet in agreement that "their" is a determiner by the rules of prescriptive grammar,
No.- both "it" and "their" are possessive references to something or somebody mentioned before or which was otherwise understood. (referents).