I think it’s mostly about hormones affecting their instincts. In a human female, nursing generates hormones that causes the milk to let down.
Years ago when I was quite young, I had a cat who had kittens, probably too young, and the kittens were obviously premature. They seemed to be unable to nurse, and the mother cat took no interest in them.
I tried to induce them to nurse, placed them in the right position and even tried to put their mouths to the nipples. One by one they died, in spite of all I could do. Offering them an alternative to their mother didn’t work either.
For a brief time, one of the kittens was finally able to attach to the mother and tried to nurse. For a little while after that, the mother showed some attachment to this one, cleaning it and showing maternal interest. When the kitten didn’t get stronger and the nursing didn’t continue, her interest died. From that observation I felt that the nursing created the instinctive maternal feelings, so perhaps when a different species begins to nurse on a lactating female animal, that same instinct occurs, irregardless of the species.