I might be misunderstanding the problem (sorry!) but Sync Gen won’t sync the notes coming out of your host - it is only for providing clock to external hardware that receives MIDI clock (or DIN Sync) for some purpose - running an internal sequencer, or syncing LFOs.
It doesn’t know anything about the notes you are sending from Live to the Rytm.
For that you would need to set an offset to compensate for any delay sending notes from Live > Rytm, and the sound coming back in to Live. Depends on sound card settings, but 256 samples will result in ~18 ms round trip latency (the amount you’ll need to compensate for).
For tighter recording you’re better off sequencing on the Rytm.
FWIW I use Sync Gen to slave Cirklon to Logic on a Mac. There is always some jitter when I hit play in Logic, while Cirklon attempts to sync. I haven’t looked for a solution, just assumed it was normal. After the initial 1 or 2 beats of jitter, sync is perfect (but I’m not sending any MIDI from Logic, that’s all handled by Cirklon).