if you added, removed, or changed positions of spacers, you may have removed required gap between top of steerer and cap. it will create an illusion of a properly adjusted headset when in fact there is none.

AFAIK there is no difference in proper adjustment technique as regards integrated vs. non-integrated headsets.

OTOH, it may not be the headset at all. stuttering as a result of braking could be caused by a number of things. if ONLY noticeable when braking i might start looking elsewhere for problems.