Water shooting out the exhaust is normal when you pull the ski out of the water and put it on the trailer. In fact, every time you trailer it, you're supposed to start the engine and give it a couple short revs to blow the excess water out of the muffler. That goes for after you flush it on the hose too.
Next time, avoid attempting to start the ski when hooked to a battery charger. That can damage the electrical system of the ski. Its OK to use jumper cables as long as the vehicle your jumping with is not running. The idea is a charger or running vehicle is putting out more than 12 volts and can cause problems. When using a battery charger, its better to charge the battery with the ground cable unhooked.
If possible, make sure there is no water coming out of the spark plug holes when you crank it. Hook spark plug boots to the grounding posts on the E-box, take out spark plugs, and crank over to see if water shoots out the holes. If there is water in the engine, you want to get it all out before resting tonight.