The garbage disposal should be plumbed into a waste tee so that when you turn on the disposal the refuse is injected into the main drain at about a 30 degree angle. If the discharge from the disposal was improperly installed, the end result is undesirable.
My disposal does this too. It started when I replaced the pipes under the sink. The old "T" pipe that connects the disposer to the other sink had a baffle thingie that forced the disposer discharge down toward the p-trap. The new one lacks that feature. I don't know if it's available.
Your drain line may be clogged. When this happens, the food from your disposal can not go down the drain, and will be forced up through the other sink.
There is probably a clog in the drain after where the two drains conjoin below the sink. If this is the case the food is being backed back up into the other drain. should be a simple fix just snake the drain.