Craig said that you need to find out what is causing the duplicate notes. I agree and found in my case, the dreaded COPY and PASTE while in PRV was causing my problem. And, have discovered that whenever hit the the CNTL V to paste midi notes and the paste looked like it didn't work, I now instantly hit CNTL Z to UNDO the paste. This odd copy and paste thing has been plaguing me for years but will say the above has eliminated by duplicate note problem.
My theory is that somehow SPLAT is losing focus on the track I am editing in PRV. Or that I don't know what I am doing (which could be the case). Either way, the above CNTL Z has eliminated by problem.