Being new to the Fractional business, I can only speak for myself and from what I've heard so far...
Most pilots do not fly on their days off since you'll be fairly burnt out by the end of your 5-8 day rotation. However, if you choose to fly on your days off, if it's commercial flying it must be reported to crew scheduling in order to keep accurate records for Part 135 requirements. Other flying is at your discretion, just don't let it interfere with your ability to report for duty!