Nope, neither Augustine nor Aquinas contradict themselves, nor is it the case that God “causes” our actions. God empowers us to act freely, thus underwriting our moral agency by making it ultimately possible. That does not imply God causes our choices, he causes our freedom to make free choices, but the choices themselves are completely ours to make.
The quote from John means that the Father draws us to him, but that does not imply we must follow that impulse. We can resist.
In fact, as long as God makes sufficient grace available to overcome the power of sin over us – i.e., that the Father’s “drawing power” towards him sufficiently balances out the drawing power of sin away from him – then the onus, responsibility and blameworthiness is completely upon us since we could equally have chosen to be drawn to the Father as to be drawn away from him by sin. By underwriting our capacity to choose, God does not necessarily cause our choices. He causes our choosing but not our choices.
Read both Aquinas and Augustine again. When Aquinas, for example, is speaking of God as “the cause of these in things” he clearly means God is the cause of the “operative powers” (i.e., the operative power of free will) in these created things (human beings, Angels, moral agents, etc.). And by “…Every operation, therefore, of anything is traced back to Him as its cause…” Aquinas means every free operation of the will as a free operation by the moral agent, not as causal determiner of the choices by that agent.