You do realize that when you shut off a car that's been run, the hot exhaust system cools.
When that VERY hot exhaust manifold, cat, pipes, and muffler cool, the air inside the muffler, pipes, and cat cools........as the air cools, it condenses. Then the exhaust system draws in outside air and condenses that, too. The drawn in air condenses throughout the system and forms water which pools all in the ssytem, esp. in the muffler. And the muffler is the last piece of the exhaust system to fully heat and evaporate the built up pooled water. It's not unusual to see a cold car/truck with some "steam" and water dripping from the tailpipe when the exhaust system is heating up.
(This condensing of the air into water and the water pooling in the muffler is the chief cause of mufflers rusting from the inside, which is the main rust problem for mufflers. This is why GOOD muffler manufacturers, like Walker, promote and trumpet their resistance to rust-through. Someone who drives nothing but in-town short trips never heats up the muffler fully to rid the exhaust system of all the water that's collected inside.)
If, after 10 minutes of driving, you continue to see vapor being emitted from your tailpipe, you may have a problem. Watch your cooant level. Check your oil, too. Cracked heads sometimes allow the oil and coolant passages to communicate and your oil will become milky. Sometimes you'll find an oil sheen/dropplets floating in your coolant.
Otherwise, if the symptoms disappear after some driving, it's probably normal. Water dripping from your tailpipe, esp. when it's just heating up, is pretty normal.