KingOfAnything found the relevant FAQ.
Point being that "arcane spellcaster level" =/= "caster level".
The first is a reference to CLASS LEVEL (and "effective class level")
of the class(es) (or other source) which granted the Familiar ability.
"Caster Level" is a distinct mechanic, even though levels of spellcasting classes also grant it.
There are various mechanics outside of class level to boost "caster level" (e.g. Ioun Stone)
but those don't help get higher tier Improved Familiars or boost Familiar abilities.
AFAIK, even full caster level PrCs don't advance Familiars...
(unless they explicitly state so, or Familiar is gained from non-Base Class source like Feat... which utilize ALL levels, even Commoner)