I think that this is where our opinions diverge, Sir toodeep, because my read of the text tells me fairly clearly you do not get the tradition. The text of the spell Commune with Spirits says:
Commune with spirits wrote:
. . . this boon takes
the shape a single spell from the
Corpus, Illusions, or Control
Traditions.
It does not say that "You gain access to the Corpus, Illusions, and Control Traditions and the ability to cast one spell from one of these three traditions for 24 hours", it simply says you gain access to a single spell from the tradition. Because there is a VERY long list of spells in those three traditions, it makes much more sense from a word count perspective to just say "You can choose a single spell from the list provided later in this document" rather than individually listing each out.
That said, while you get to choose a single spell from Corpus, Illusions, or Control, none of those Traditions are playable for Primals. In fact, that is one of the core concepts of their casting options. As such, you gain access to one of these spells through a SPELL, not through the base tradition. Your "Tradition" for the spell gained is "Commune with Spirits" because you have not received training or access to the actual tradition that they originally came from. The metanarrative reason for Tradition, Path, or any other special adaptation is that by learning that spell through that method, you are taught new ways of manipulating it. It is the same concept as a Secret or Exotic spell. Since you do not have this training, but simply gain the power by selling your soul to a quasi-divine being, you do not have access to this special training.
I could be wrong, and if so I'm sorry, but my reading of the text does not support the argument that you 'gain the tradition along with the spell.'