"On my last two flights as I was paying attention to the safety briefing and the instructions were, if using the overwing exit to inflate the life jacket after leaving the aircraft. Previously and at another carrier the instruction was to inflate the jacket as one was leaving the aircraft."
Firstly I'm not CC, but an unlicensed avionics technician so I am not offering this as a definitive answer, but what I believe to be a logical explantition for the difference.
If you are abandoning the aircraft from an overwing exit the chances are that an inflated life jacket will severely hamper your progress, or perhaps even make it impossible to get out. Working on aircraft in heavy maintenance I have used overwing exits to access the wing upper surface and believe me it is not the biggest aperture in the world.
Whilst I don't claim to be sylph like, by any stretch of the imgination, I do manage to exit and enter the aircraft without any problem. I would, however, not want to try it with a inflated lifejacket increasing my body diameter by several inches.
Exiting from a main entry door is another matter. Inflating the lifejacket AFTER reaching the door threshold and then exiting the aircraft should be no problem.