Does "associated with" imply a certain hierarchy?

Good question.

I think there are three scenarios (not considering the 'spend time with' sense of 'associate with'):

(1) non-commutativity (ie the order A is associated with B is not reversible):

I am associated with Macrosift.

(2) commutativity, both syntactic and semantic:

Wealth is associated with freedom.

(3) commutativity, syntactic but not semantic

Klausenheimer was associated with (involved with ... / instrumental in) the Monhittan project. (Though note that the 'reckoned to be involved in' sense, almost the reverse of the next sense, is an alternative reading here.) ...

The Monhittan project was associated with (regarded as being the brainchild of) Klausenheimer.

All these senses are available. If context does not differentiate, a rephrasing is advisable.