With Aegeus, she uses her skills as a bargaining chip and takes advantage of the king's soft-heartedness to win a binding oath from him. Against Jason, she uses his own shallowness, his unmerited pride, and his desire for dominance. She plays the fawning and submissive woman, to her husband's delight and gratification. Jason buys the act, demonstrating his lack of astuteness and willingness to be duped by his own fantasies. Just as he has successfully convinced himself that his marriage to the Corinthian princess is a noble act, he accepts Medea's submissive woman act because it is exactly what he wants to believe.
Manipulation is more complicated than simple lying.
With Aegeus, we see Medea use the partial truth to achieve maximum advantage for herself. In these various manipulations, we see the depth of Medea's cleverness and skill. But we also are reminded that Medea is barred from the highest circles of power. Her cunning manipulation of others is the act of a desperate woman, outside the structures of power and the bonds of kinship. We are reminded of Eleanor Wilner's comment that Medea is a Machiavel without a kingdom to rule.