Snubber causing more problems than benefits
I don't know where you got that circuit(r2,r3,c1), but IMO it is rubbish.

Think of what happens when the foto-triac is not conductiong. In effect you can remove it and R2 from the circuit. Now you have the gate of your triac triggered via R3/C1, which delivers a phase-shifted current through the gate, 'conveniently' non-zero when the triac voltage is zero, thus switching the triac on after each zero-crossing, eactly as you observe.

The function of a snubber circuit is to suppress rapid voltage transients, which would otherwise cause the triac to start conduction. But at the same time the snubber circuit should not conduct so much current that it causes the load to be switched on. The trouble with your 'snubber' for the foto triac is that it conducts so much current that it always triggers the triac.