why is cold air blowing in the air handler closet?

You have a leak in the duct work. Start where the duct work hooks to the air handler and start looking for leaks. In fact, do what ever you can to check out the ducts in the entire system. Including any ducts in th attic or basement. Make sure you check any joint, including where the duct hooks to the vents.

Repair any leaks you find.

Congratulations! You may have just found a very cheap and easy method of making a major cut in your AC bill.

the plenum isnt sealed properly. most plenums are molded sheet metal and wrapped in a insulation blanket then sealed with aluminum or duct tape. also a product called mastic is used to seal the bends, folds, and leaks, in the sheet metal.

as you know, you want all the refriferated air going into your ducts and not you mechanical room. so sealing it up will make a big difference in unit efficiency. GL with it!

that means an air leak, there should be no air leaks, if is a small air leak, then get duct tape and cover it. if you have a duct that came off then re-attach it. thats all and easy to fix

You have leaks in your ducts. Get some foil tape and seal them up. Wasted AC.