I dug in to the operating manuals again regarding the use of TRs and found some interesting details and differences...
On the 550 manual, there is a description which states the following: "The nose wheel must be on the ground before actuation of the thrust reversers to eliminate the possibility of FOD and improve directional control." This is a fairly mild statement which focuses more on protecting the engines than a major safety issue.
On the 560 manual, in the exact same section, the statement was updated as follows: "The nose wheel must be on the ground before actuation of the thrust reversers to reduce the possibility of pitch-up and liftoff, and to improve directional control." This is a pretty significant statement, indicating you might find yourself airborne with the the TRs deployed, out of airspeed and options simultaneously. That's a big deal.
In both airplanes, the Landing checklist calls for Throttles to idle, Brakes applied, Speed Brakes extended, Thrust Reversers deployed, in that order.
My initial training was on the 550, then I transitioned to the 560. I think this is why the training captain during my initial training talked about the nosewheel and TRs more from a directional control perspective, rather than the possibility of becoming airborne with TRs deployed. The 550 manual addresses the issue differently and that's what we were flying.
I also think about the practical side of landings...if a pilot applies brakes and speed brakes after touchdown, THEN thrust reversers, per the checklist, I can't imagine a scenario where the nosewheel will still be in the air unless the pilot is really hauling aft on the stick. I've never flown with a pilot who threw the TRs out the moment the mains touched, before using brakes or speed brakes.