I've just had this problem crop up in the past week.  I will try to roll my aircraft left or right, and when I physically move the joystick, the controls in the VC move in conjunction with my physical movements, but the aircraft will not roll, then after a couple seconds, it moves dramatically.  This is obviously extremely frustrating.  I have re-calibrated my CH HOTAS numerous times, turn the sensitivity all the way up in FSX, as well as removed the null zone.  I also added the stick sensitivity line in the FSX.cfg.  Does anyone have any idea what it causing this?  It is happening in all airplanes, and only to the roll axis.

You can close this, or marked it as solved.  I found the solution HERE.

Had the same problem when I was using OPUS but it kept reocurring so I use ASN instead now and my controls do what I tell them to do without intervention from 3rd party software.