I've towed with both my 2017 Titan's with no issues (beside the known shifting frustrations). One trailer was 2000 lbs and the other upwards of 6000lbs. Anything is possible, but I haven't heard or read of any complaints about this transmission from a mechanical standpoint as a vibration coming from the transmission would suggest. I think this engine/transmission combo was pretty well mechanically vetted during its 7 years in the Nissan Patrol and INFINTI QX. Most complaints seems to be related to the ECM/TCM tuning. But I'm sure that provides little comfort to someone that has an issue.
There are lots of other factors to consider...maybe tires issues under load, rear dif, or simply a vibration being transmitted through the truck from the trailer. Did you tow this setup with another vehicle before buying the Titan? Have you towed anything else with your new Titan? Does the vibration change with speed or fad in and out? Is there an accompanying noise? Does it change based on the road? Is ther any hint of vibration when not twoing? Is the vibration felt more in the floor or the steering wheel? is the vibration the same when on the gas, off the gas, or on the brakes?