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.

Let's talk order magnitude for ease of understanding. Say your high voltage side is 50Hz mains power. In that case the reactance of the capacitor is:

\$X_C = \dfrac{1}{2\pi fC} = \dfrac{1}{2\pi\cdot50\cdot 47\cdot10^{-9}} \approx 68\text{k}\Omega\$

As the capacitor's reactance is much higher than R3 and therefore we can safely ignore R3 for sake of this discussion. Also the maximum gate voltage will be in the order of 1V, which can again be ignored with respect to eg. 100V mains voltage.

If the mains power is 100V then the gate current of the TRIAC will be approximately:

\$I = \dfrac{U}{X} = \dfrac{100}{68\text{k}}\approx 1.5\text{mA}\$

For an average TRIAC 1.5mA is sufficient gate current to trigger it and the photo-TRIAC has no part in it at all. When using a 230V mains, the current will even peak at approximately 5mA. As Wouter mentions in his answer aswell, the current calculated is shifted in phase with respect to the voltage across the TRIAC, causing the TRIAC to reliably trigger.

I am unsure why C1 was included in the circuit. The TRIAC doesn't act as an inductive or capacitive load, so there is little need for a snubber arounc C1 anyway. The other snubber C2/R4 can be much more benificial, although a snubber should ideally be dimensioned for a specific load.