As I understand it, even though SSRI's are supposed to act on serotonin, they also affect dopamine levels because serotonin modulates dopamine. Too little dopamine can cause tremors, spasms, and other motor control issues (Parkinson's, tardive dyskinesia, etc.). You may have noticed this when you first started on fluoxetine, before your body adjusted to the medication.
Several kavalactones act on dopamine levels, also, lowering and raising the concentration depending on dosage. I'd be willing to bet that there is a chemotype out there that will greatly reduce this effect, but since it seems like we really don't know the exact actions of the kavalactones, it's difficult to make any recommendations (and I can't remember at the moment which one is supposed to exhibit the most dopamine antagonism). The weird thing is that MAO-B inhibitors, which some of the lactones are believed to be,
should help with the twitching.
If you decide to keep drinking kava, keep us updated on which strains affect the twitching! I'm super interested in this sort of thing, and it's helpful knowledge for shellers everywhere, as a huge number of folks are prescribed SSRI's (including my girlfriend, which is one of the reasons I did so much research on this particular subject to begin with).