Hi and welcome to Arturia forums.
Yes you will not hear any Sync if you set the mixer fully to the Second line. You need sound from the First line, but not from the Second line as it is.
I think it's because (the problem) is that OSC-1 (First line) is being synced with OSC-2 (Second line) instead of the other way around (like it is in Mini V). That also means you can't use the original detune parameter to create harmonics as it control the OSC-2 tuning.
As it is you need to get the sound from First line to hear any sync. And detuning has to be done to OSC-1. That can only be done thru the modulation matrix.
I don't know if the LINK synth lines feature have anything to do with how it's done. But OSC-2 should be Synced with OSC-1 to have the option to use the original detune parameter to create harmonics, and still keep an option to use the modulation matrix - also for OSC-2 instead of for OSC-1.
And then the combined sound should still be routed to Line 1 so you also can use the the LINK synth lines feature, or this LINK feature should be routed to the Second synth line instead. I don't know if there is a routing problem, but to me it's a shame,that you can't use the original detune parameter to create harmonics when using SYNC.
That said, then the SYNC feature was'nt on the original Yamaha CS-80 hardware synth. It's an extra feature. And the SYNC work - just not with the original detune parameter. To me this is a construction failure.