Your line here that, “...the bath themselves were dedicated to Minerva ,a healing deity .” is the problem (as ED has eloquently pointed out). It’s a fine distinction but an important one. We could equally say that such and such a church is dedicated to St. Francis who preached to birds... (you can fill in the rest yourself :-)

Your linking of Minerva to a healing deity implies (perhaps unintentionally as I said above) that the healing aspect of the deity was the primary reason for the springs being dedicated to her. Again we do not know that to be so, though that aspect/role/manifestation of the deity would no doubt have, among other manifestations, been worshiped there.