I found that if I undertook only that mission (i.e. didn't also sign up for normal get this commodity, take this message, etc) then the ranking worked as soon as I completed the mission, either back at the originating station or the destination if it was a courier type. The only times it didn't work, I already had missions on the books (so to speak) or took another mission at the same time.
In the end it was ridiculously easy to get to Post Captain and after 1.3 up to Admiral - (no promotions to 1st sea lord or admiral of the fleet LOL)