I don't know too much about the au but do you think mizuki uses tama as a way of feeling keeping a piece of date around?
it's a little surprising that they never mention tama's appearance in AINI, isn't it? it's so heavy on 'show and then tell' but there's not even the same oblique "modeled on your preferences" line aiba gives in AI1.
anyway, the 18 year old mizukis i'm drawing are post date-as-boss dying and therein post the dissolution of ABIS, the only AI-balls that don't remain with their owners in that circumstance are aiba and tama for obvious reasons, mizuki and pewter are the only ones involved in the off-the-record ABIS operation being run out of saito's old murder den, the girl gets both AI-s in her ball, i just draw her with tama more often.
as for why that is, the boring watsonian answer is "tama is usually the one on mizuki's good side because she's more pro-murdering saito" and the boring doylist answer is "i think mizuki getting aiba in aini was a weird bad choice because they're both very similar characters designed to play against Date, her dynamic with tama is more interesting to me both in general and because we never get to see it in game"
as for what i think... the idea of the AI-ball is a very interesting space to play in, both where it's adequately constructed in AI1 and where there's a mess of unaddressed implications from it being retrofitted into the almost sort of sci-fi wish-fulfillment role it takes in AINI. looking at the whole picture, both aiba and tama are 'a piece of Date' in a way: an actual closeness and a healthier answer, or a superficial similarity and an easier answer... something like that?