noise - Triac spurious triggering issue

I have a circuit where I am using triacs to switch home appliances like fan, tube light etc. This is the circuit I am using:

(TRIAC1, TRIAC2, TRIAC3 come from arduino GPIO pins)

First load is a fan with a capacitor based regulator. (Sorry for showing fan and tubelight as a resistor). Speed is controlled by rotating a knob which changes the series capacitance. Lower capacitance means lower fan speed.

As seen from the circuit, I didn't use a snubber because I thought using a snubberless triac will do the job, however the following incident made me rethink about the situation:

1) When Bulb and tubelight are off and fan is ON, and I try to regulate the fan speed by rotating the knob, sometimes there is a flicker in the tubelight and bulb. Flicker is very short lived but still visible. Flicker doesn't happen at higher speed. It usually happens at lower speed levels. For ex - There are these levels: OFF, 1, 2, 3, 4, 5 (5 means direct connection to Live). When I switch speed from 2 to 1 (or vice versa), I see a short lived flicker in the tubelight.

2) If the fan is running at low speeds - 1 and 2, and I try to turn the fan OFF by pulling the GPIO (TRIAC1) LOW, the fan won't turn OFF. Instead it produces humming sound and continues to rotate at a lower speed which indicates partial turn ON of triac.

Now in order to fix this, I am planning to use a snubber. I read a few articles and this is the circuit I could come up with:

Rs and Cs are usually mentioned as 39 ohms and 0.01 uF respectively. However I have a few questions:

1) Is my assumption of spurious triggering correct? If yes, will the proposed circuit improve the behavior?

2) Usually snubber design for inductive load shows a pure inductor as the load and a parallel RC circuit as the snubber. Here, the load is LC due to the presence of capacitor based regulator. Should there be a modification in snubber circuit due to this?

Here is the fan regulator I am talking about:

EDIT:

Fixed the snubber circuit.

Added the image of fan regulator.

UPDATE:

Tried the snubber. It didn't work. I am assuming some sort of resonance when the regulator is kept at low speeds. This resonance might be preventing the triac from turning off completely.