No, IIRC, it's only based on which game you are playing. After their base stats in BG they improve once for each game, twice in all. At the start of BGII, and at the start of ToB.
So starting in BGII they will only improve once you reach ToB.
I tried the mod Afaaq, it's a "familiar npc" a seventh member of your group, and he improves as your main character gains experience. It's a surprise if no mod tried to improve familiars in such a way.
Does your familiar improve if you summon it in SoA then continue into ToB? I'm pretty sure you don't get the extra hit points, but does your familiar improve to it's ToB version, or only if you summon it there?
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So starting in BGII they will only improve once you reach ToB.