In most citations with TR's you will find in the AFM that it reccomends a push due to the pitch up action of the buckets deploying.
CJ's and 525A/B dont have reversers, some have attenuators so its probably a throwback from a previous jet, max TR deploy speed in most 500 citations with them fitted is around 125knts, at these speeds you will definetely need to push, if the speed is back and say inside of say 60knts ish then the other chap might have been pulling back to mitigate the nose dive from heavy braking to make the exit, probably just thinking about pax comfort.
If you deploy at high speed and then pull you will probably scrape the thail!!!
Incidentally there is a great video of a 500 deploying one side in flight at 150knts somewhere - bit of a wild ride!!