Role of ATP and AMP in functioning of Phosphofructokinase
This is clearly explained on the Wikipedia page for glycolysis under the heading Phosphofrucokinase. AMP is an allosteric activator of the enzyme and ATP competes for binding at the same site but is not an activator.

You should think of the interaction between the two regulators in terms of reversible binding of both: since they compete for binding at the same site the proportion of the enzyme with bound AMP will go down if [ATP] goes up, for example.

Neither of your proposed schemes is   correct: the enzyme is more active with AMP bound and less active with ATP bound. The idea that AMP binds, activates, then wanders off is wrong.