Cambridge definition of "ultimatum":
a threat in which a person or group of people are warned that if they do not do a particular thing, something unpleasant will happen to them. It is usually the last and most extreme in a series of actions taken to bring about a particular result.
Was it the threat he made to Conklin that if he didn't leave Bourne alone he would turn the fight around?
Which he does in the 3rd movie, he exposes Blackbriar and finds out who he is by the end.