There can be a few different reasons causing your sink to fill up with water when you run your dishwasher.
Clogged Sink - A kitchen sink clog could prevent your dishwasher from draining properly. You might be able fix the clog by running the garbage disposal, plunging the sink, or snaking the drain.
Air Gap Blockage - Air gaps are installed in kitchen sinks next to the faucet. An air gap prevents wastewater from backing up into the dishwasher. If water is flowing in the sink from the air gap, look inside it and remove any debris causing the block.
Garbage Disposal Drain Plug - The drain plug covers the hole connecting your garbage disposal to your dishwasher. Sometimes when a garbage disposal is installed, the drain plug is not removed. Simply remove it from the garbage disposal to resolve the issue.