Drain tubes make the draining happen. All the wastewater passes through them to the drain. If they are clogged, the dishwasher can no longer drain any more water coming out of dishwasher air gap.
Sometimes, the junk or particles block the tubes; mostly from where there is no steep to allow them to fall freely. From a tiny piece of food, it converts into a large amount of food debris in a matter of time if the drain tubes are not cleaned after regular intervals of time.
Even grease can clog the drain tube if not cleared fully. This can cause a blockage in the way of draining water and hence a leakage in the air gap takes place as the water flows backwards. You can remove the grease by passing hot water through the tubes. You may clean the tubes or replace them with the new ones and the problem will be solved. Keep in mind to regularly make sure that there is no blockage in the draining tube for your dishwasher to drain properly.