Leak Under the Sink - possibly air gap related

I purchased my first home last September, and my wife and I have now just entered the "do it yourself" world. Our home was built in 1948, and a remodel was done to the kitchen back in 2000. This included a new sink, cabinetry, and appliances. On Tuesday we discovered a leak underneath the kitchen sink, which we eventually determined came from the faucet (a Price Pfister model). We went to Home Depot and purchased a Kohler model, which we installed. The sink works perfectly without any leaks, and we're satisfied with the product.

After running the dishwasher, though, we came across a new problem. Water was spurting out from either the out-going or in-going tubes connected with the dishwasher air gap. (I say "either", because I honestly can't determine which tube is causing the problem since they are so close together.) I looked on-line to find solutions, but all of the problems pertaining to dishwasher air gaps appear to be when water comes out from the top and drains on the counter or into the sink. My issue is underneath the counter. We've tightened the tubes, we've unscrewed the tubes and replaced the air gap with a new one -- we just can't figure out what the problem is. I don't know if there is a small tear in one of the tubes (most likely the in-going), or if there's something to do with the garbage disposal.

Any thoughts would be greatly appreciated!

If you have already replaced the air gap, I'd replace the tubes. Likely one is split, as you suspect.

How about trying to test the in-going first if the water will still spurt out. We got the same problem before and figured it out by checking them separately. Just try it.