Not to sure about a 2009 Seadoo's fogging, but all models I've ever worked with, come with a plug in the air box that you use to insert the tube for your fogging spray.  You fog while the motor is running, just before shutting down.
Using 2 stroke oil?  If that were the case, then we would not have to fog our 2 stroke motors at all, since our cylinders are coated with 2 stroke oil on a regular basis.  I think you are mis-quoting.  The dealers said you use the same fogging oil as they do in the 2 strokes, but it's not really a "2 stroke" oil.  The fogging oil is more like a sprayable grease, that sticks to the cylinders over a long period of time.  The reason you do it is to protect the cylinders from moisture build up.  If you have un-protected cylinders, rust might be able to form on them.
I live in the deep south of the U.S. and really don't need to fog for Fall and Winter.  I do start and run my motors once every couple weeks.  I did have one motor that was a spare, I fogged it with spray on "Lithium" grease.  Lithium is commonly used by mechanics when assembling a new motor to protect the surfaces from the elements.  When you start the motor, it's washed and burned by the gas for combustion.