no, you're mistaken. it stays at the same level as summoned until it is resummoned with the new level. to add to that, for anyone who doesn't know, the affects of the new level won't take place until the old aura's bonuses completely wears off, only then will the new level apply.

only spirits stay at the same level, pets such as bears, ravens, wolves, oh my, do not stay at the same level when gear is changed