C525B pilot reported a suspected autopilot pilot malfunction and erroneous trim indication during climb out.

Narrative

Day 0 Aircraft RTS (Return to Service) ZZZ airport to ZZZ1 airport deviation On just a couple hours notice; I was told by my company to airline from ZZZ2 to ZZZ3 to pick up Aircraft X coming out of maintenance in ZZZ to fly single pilot to ZZZ2 to replace another aircraft downed we had there for a customer flight the next morning back from ZZZ2 to ZZZ4. After quickly packing my bags and going to an FBO at ZZZ2 to get my headset out of the aircraft; then went to the ZZZ2 terminal to catch a XA:25 flight to ZZZ3; then rode to maintenance at ZZZ airport; I was notified by the maintenance technician there that Aircraft X wouldn't be RTS (returned to service) for 'at least another hour'. Thus; I borrowed the crew car and grabbed dinner. By the time I was called at XD:30 to come back to the RTS'd plane at the maintenance hangar; the sun was already starting to set. After pre-flighting (including checking the aileron trim position which is notoriously always a bit off center in every Cessna CJ airplane I've flown over the last 8yrs) and calling the company to verify I was good to takeoff per the maintenance log signoffs; I got the clearance (Depart runway XXL right turn heading 120 degrees; climb to 4000); taxied out; and took off (approximately XE:24). Being single pilot; I turned the autopilot on after 400ft; navigating the in Heading mode and climbed the airplane in Vertical Speed mode at roughly around 220+kts. At about XE:27; still in the long turn to heading 120 and sometime after climbing through roughly around 3500'MSL -with no warning on the PFD (Primary Flight Display) to correct trim error- the autopilot suddenly kicked off and the airplane lurched into a very hard right bank. I quickly put the autopilot back on thinking initially it was only the autopilot turning off due the turn I was in in combination with the turbulence I was going through (which I have experienced occasionally in previous flights) and that the airplane had caught some sort of updraft that kicked it hard right. The autopilot and airplane immediately shutoff and lurched very hard right again. It actually took a surprising amount of opposite yoke to oppose the force and I thought for a moment that maybe I was experiencing a flight control failure or locking of some sort since it just came out of maintenance and maybe a tool had got jammed or something (anything can happen post-maintenance and that's always a mental factor in the back of my mind on these flights). I announced what was happening to the controller that I was talking to when he happened to call me at the moment. Somewhere in that short amount of time of those concurrent series of events; working through what was suddenly happening with my flight controls at this altitude that didn't happen in the few couple thousand feet; I blew through the 4000 ft altitude and neared 4500 ft. My priority was aviating; not navigating. I ultimately quickly trimmed the aileron trim left to adjust it to a more reasonable position; and lowered the airplane back down to 4000 ft while talking with the controller through the events. The controller asked if I needed to declare an emergency given the flight control issue and I responded no and that I had just gotten the trim worked out given the airplane had just come from maintenance. He seemed to be understanding and passed me onto the next controller for the remainder of my climb.In retrospect: Every CJ pilot will tell you that no matter having checked the trim position indicators in the checklist process; they all have had to deal with trim setting issues one time or another during flight on climb out or level out after it's come from maintenance or sometimes even after other flight crews have flown the airplane in a normal rotation. It was not prudent for me to follow through with the reposition flight given the airplane RTS got pushed back two to three (first XB00; then XD00; then XD30+) different times and now I was faced with a single-pilot;post-maintenance flight; in the dark; over harsh semi-mountainous/desert terrain with some amount of cloud activity and turbulence; into a class B airport. I could have stayed the night at ZZZ and this RTS flight could have waited till more optimal morning daylight conditions for this post-maintenance checkout but the company was pushing to get the flight done that evening so that if there were any remaining maintenance issues; they would have had ample time that night to find the next morning customers adequate alternative rides home. The company should not pressure an RTS flight to be done at night just so they have time more time to accommodate a pax (Passenger) repossession flight if necessary. Instead RTS flights should be done in conditions that are optimized to the pilot/plane/WX. Post-maintenance RTS flights should not be done single pilot (the company should have airlined my co-pilot out with me). It would have been beneficial to have had a co-pilot there to have pushed back on the flight controls; work the trim adjustment; or monitor altitude/heading. Post-maintenance RTS flights should not be done at night. The company should have a post-maintenance RTS line item in its FRAT (Flight Risk Assessment Tool). In combination with all the other factors; that would have triggered an alert signal to reevaluate the flight and possibly bring in other members of operations to look at the situation.The aileron trim on an aircraft in a good flying trim condition is slightly to the right of center.