I will share a little, and there will probably be others that can give better detail with more experience.
When riding, there is a portion of the water that is pushed out the jet pump to propel you forward, routed thru a hose into the exhaust manifold and cooling chamber. You could estimate about 95% of the water goes thru the jet pump out the back of the ski and 5% is pumped, under pressure, into the exhaust manifold and cooling chamber. The exhaust from the engine pushes the water thru the manifold, cooling chamber (that large metal canister) and out the exhaust hole near the jet pump.
Your flush from a garden hose does what the jet pump does when you are riding. The ski hose routing to the exhaust system may route slightly differently than the jet pump cooling hose. You can probably find the hose in the hull where you attach a garden hose and follow it in the hull to where it attaches to either the exhaust manifold or cooling chamber. I think on my 2007 GTI SE 155 the garden hose water goes into the cooling chamber, not the manifold, but not 100% sure. But the point is, that your garden hose is cooling the exhaust, and flushing out lake water, salt water, possible organisms in the exhaust, etc.
You are probably beginning to tell that it is critical to have the engine running, providing the exhaust pressure pushing water thru the exhaust cooling system, before you turn on your garden hose. Because of the engine isn’t running, you will fill the exhaust manifold and cooling chamber with water, and then water will back up into the engine, going into cylinders with open exhaust valves, and leaking slowly in cylinders with closed exhaust valves. This creates the Worst nightmare for any ski owner - a water filled and locked cylinder or two. The engine won’t be able to turn over, and the compression stroke pressure in the cylinder pushes the water past the piston rings into the oil crankcase at the bottom of the engine. And it sucks. I know all about it when my ski cooling hose from the jet pump to my exhaust manifold came off in February and so water (salt mind you) was not getting to my manifold and was filling my hull up until I sank. Long story…but it has a happy ending. You can read my posts from February and March this year if you want a nice bedtime story. Hope this general description helps - someone with more knowledge can maybe explain exactly where the garden hose flush connection on your ski comes into the exhaust system.
And yes, there is a Venturi effect that you have to be concerned about when towing a disabled ski that is not running. Read the owner manual for your ski. There is a speed limit you should not exceed, or on older skis they recommended you pinch off your hose from the jet pump to the manifold, to prevent water from working its way into your exhaust manifold with the engine off, causing the same water locked engine situation I explained from the garden hose.