Consider what you are thinking about actively as being in the "front" of your mind. Those things that you think about on occasion, or when the "front" of your mind is not busy, are in the "back" of your mind.
In this case, the man has not decided to quit his job just yet. But part of his mind is thinking about quitting, and it influenced his decision.
(Just to be clear, "front of the mind" is not an expression, I used it to explain "back of the mind.")
- For Teachers