How did she actually manage to travel back in time and actually end up in the delta quadrant from the alpha quadrant instantly using the chrono deflector?
As you say, she used a chrono deflector, which works by using a tachyon pulse to form a directable temporal rift.
The device operated by generating a powerful tachyon pulse to form a temporal rift, which could then be directed to a specific time and place. Although able to generate a stable rift, the device also produced a large amount of tachyokinetic energy as a byproduct of its operation, posing the risk that it would burn itself out after a single use, prohibiting a return trip for the user.
Tachyons are particles that travel faster than the speed of light. If such particles really do exist, it's possible they could indeed be used to facilitate time travel:
Here's the temporal rift: