I have a dual bowl kitchen sink. The nondisposal side drain sits higher than the disposal side. The disposal drain connects to the nondisposal drain horizontally via a tee pipe. Sometimes when there is a lot to grind in the disposal the ground contents will shoot up into the nondisposal side then recede on down the pipe. My old house did not do this but the disposal was connected vertically to the nondispsoal drain. Can this be fixed (no shooting up of ground stuff in the nondisposal sink) with a horizontal tee joint? See attached image of my configuration.
The cause of the water shooting up through the other sink is not caused by the disposal being on the lower sink. It is because the plumbing is not set up correctly.
When using a disposal you need to have slip joint baffle tee with tail piece. The baffle is inside the tee and it directs the water, that is being ejected from the disposal with force, downward.
With out the baffle the pressure is to great and the water will shoot the wrong way.
In the photo below the water comes from the disposal on the right, the baffle is in the tee. When the water hits the baffle in the tee it is directed downwards.
The shallow sink is supposed to have the disposal on it, that's why it's a different depth. Move the disposal over to the other sink.
Does your sink drain slow too? Your drain is probably clogged which is probably the root cause this problem.
You may be overwhelming the disposal too, what's the typical stuff you put down there that causes this?