I have a mixed system of the Insteon Appliance modules running in X10/ Insteon mode and X10 Modules.
The Insteon ones are; for the most part are fine with fluorescent lights, but not ALL of them. Older types with ballasts; can restart by themselves and may flicker slightly as they cool down when turned off. One of mine with a certain light can be made to sputter and loose its programming.
I have also seen reports of some electronic ballasts not working well with them also. Mine are early ones. The replacements; from the recall; where some loads shorted them out and they smoked.
Few years ago in age.
I also believe the load rating on them is lower than the X10 ones. Many find just adding a small incandescent bulb in the circuit cures X10s flicker and restart problems.
I believe all manufacturers are going to have to release new modules to work with modern lights like LED CFL and ones that are just in the engineering prototype stages right now.