In-universe, this is a case of a self-fulfilling prophecy. To quote Wikipedia:
A self-fulfilling prophecy is a prediction that directly or indirectly causes itself to become true, by the very terms of the prophecy itself, due to positive feedback between belief and behavior.
In this scenario, 'New future' John would send back the Terminator to save himself, because he knows from being told in his past that's what he does to save his own life.
Out-of-universe, this is an example of a time paradox known as the Ontological Paradox (or, more commonly, the Bootstraps Paradox). In fact, the entire premise of the Terminator Series revolves around such a paradox. This link provides a good write up of the Bootstraps Paradox, but to summarise the part that relates to the Terminator series:
In the future, a Terminator is sent back in time to kill the mother of resistance leader John Connor before he is born. While the original T-800 is ultimately destroyed, the leftover pieces are found by scientists who use the technological to...develop and create SkyNet, and the Terminator-series robots.
Note, the T-800 is the same as the T-101, but I digress. The point is that time travel movies, by their very nature, have plot holes like this related to time-travel paradoxes. We, as the audience, just need to go with the flow, and take such things as a grain of salt.