Jason Bourne is an ISTJ. ( INTJ is also possible but not probable)
What he does is NOT improvising , CIA has taught him everything , they have shown him all the possible scenarios in that program (I think it's name was Treadstone) he has learnt how to get away from the authorities because CIA needed him to do their dirty stuffs around the world but they didn't think one day he would use his skills against themselves.
Bourne was REALLY loyal before the program , a complete patriot , also just compare him to James Bond (A real ISTP) , Bond literally lives at the moment , when he is fighting bad guys , he is also flirting with some girl , that is extroverted sensation , getting every possible outcome from the moment , not just the tactical outcome. That is a misconception about Se and it's the reason all the action heroes and even some obvious intuitive geniuses (Like Patrick Jane or BBC sherlock Holmes) are being mistyped as ISTP .
Bond's inferior Fe is obvious whenever he gets manipulated by a girl. But as you can see in Bourne's identity , his interactions with Marie and eventually loving her is a great example of his Fi.
Now i say that INTJ is not probable because He still works within the same framework that has been taught to him , in all the four movies , he doesn't change his ways and even in the last movie he still has the same style as the first movie , that is Si.