My understanding is that is different for each person and also can depend on how immersed you are into the action that you are looking to see carry over. I have done things very actively IRL and that action bled over into my dream the same night (one example I recall was a lucid, the other example off the top of my head did not lead to lucidity). Other things can take weeks or a month or possibly more.

Are you also using WBTB or some other way to help nudge along your work with SAT? I primary use awareness, reverse reality checks, reality checks and SSILD (a relatively easy WBTB method that doesn't require staying up long).