I think that is a common problem on any lathe where the spindle drive runs open loop feedback. Although the encoder index provides a start signal, the Z axis and the spindle are not electronically geared together. Therefore the time delay between index detection and initiation of motion may be a constant, which means that changing the rpm will affect the phase angle of the toolpath entry point.
If chatter is bugging me, I usually end up writing out a threading routine in full with G33 (Mitsubishi) so that I can cut alternate flanks of the thread. This decreases contact area and promotes getting the tool edge under the skin to take a cut.
Keep the cuts fairly aggressive in depth, too. You might only have the opportunity to take one or two finish passes with the tool fully engaged before chatter begins again.
Also try the miracle fluid WD40 during threading. It can make quite a difference in chip flow, reducing chatter or delaying the occurance until much later in the threading process. The trick is to be done before 'later' arrives