Jesse took the decision to come back from the future after it became apparent that John wasn't simply trying to kill all of the Terminators, he was actively engaged in two projects that she abhorred;
1) Negotiating with the Cyborg Resistance ("Will you join us?") and
2) using re-conditioned Terminators on the Human Resistance's bases.
When she learned that John had sent back a female-form Terminator (Cameron) to protect his younger self she realised that his fascination for Terminators may have been down to his close relationship with one in young-adulthood. She procured an attractive girl (Riley Dawson) and used her contacts with the brother of one of her unit to parlay a secret trip back into the past with the goal of turning John against Cameron.
Jesse: Not to me. There's metal everywhere these days. Looking for us.
Working for us. Connor's got at least one in every major base. A big
one flipped on us, took out half a bunker. Bird. Cullie. That's from
the same shrapnel that killed Cullie.
Derek: How'd you get back here?
Jesse: Cullie's brother. He's a bubble tech.
Derek: He's the same one--
Jesse: Who sent you back. I know.
The Tower is Tall but The Fall is Short