Are you sure that chuck was properly seated to the spindle when screwed on? You want it properly seated before tightening the set screws. Not doing so can easily result in increased runout when tightening the set screw(s). If you have not done so, play around with seating then chuck, then loosening, repeat a bunch of times, to develop a “feel” for how hard to seat the chuck.
I use set screws for all my chucks, as even the “perfect wrist twist” does not hold everything I do - Over the years I’ve had the chuck loosen on quite a few pieces. My lathe has adj braking, set to a high level, and I hollow in reverse quite a bit, both requiring chuck set screws to be used.