If your sink leaks when your dishwasher runs, I wouldn’t blame the dishwasher.
The leak could be coming from several possible locations.
Most likely the leak is happening when the dishwasher drains, and so start looking closely at the drain line forward. It may be a split in the drain line, but the best way to find the problem is to run the dishwasher and look for the leak.
The drain line will connect to the air gap on top of the sink, and this is a likely culprit. From the air gap, the hose runs into the side of the disposal. So if you see a leak only when the dishwasher is running, you know it is isolated to the dishwasher. If the leak is at the disposal, it would leak whenever water ran down the disposal, regardless of whether it was the dishwasher emptying into it or the kitchen faucet. Check the connection where the air gap hose connects to the disposal; this hose has a rubber boot that connects to a nipple at the disposal and it may be torn or damaged. The most likely area of the leak is from the air gap to the disposal. Check these hoses and fittings.
Once the dishwasher goes into the drain mode, the leak should be very obvious.