Had water coming on counter from anti siphon value.

My husband replaced it with a new one and checked the lines. The anti siphon value It is not connected to our garbage disposal, it goes into drain pipe. Kitchen has 2 sinks. The sink on the left had dish soap and water, and o when it drained detergent bubbles started coming on the anti siphon value on the right hand side of the sink, where the garbage disposal is and dishwasher. Ran the dishwasher and there was not any water coming out of the anti siphon from the dishwasher. Only when water and detergent are in the sink on the left. I did not try hand washing dist detergent. In the sink with the garbage disposal.

Why do bubbles come out of the anti siphon valve?

That is called an air gap, not anti siphon valve. Its purpose is to prevent contaminated water from your sink flowing back into your dishwasher. The dishwasher drain hose should be connected to the smaller pipe of the air gap and the larger pipe should be connected (by a larger hose) to either the sink drain pipe or to the garbage disposal.
Either you description is incorrect or the connections are incorrect.
When the dishwasher is draining, the water should be pumped up to the air gap. The water should them drain down by the larger hose to either the drain or to the disposal.