Yes, बिल्लियाँ (cats) is feminine in Hindi, that's the subject. Whether you say "His cats" or "Her cats," (same sentence in Hindi) the subject is still "cats," it doesn't matter who they are owned by.
And उसकी just depends on the noun that comes after it, it doesn't matter whether the person who owns it is male or female, if the thing they own is feminine it will always be उसकी.