Let it idle and to cool the turbo for a couple minutes. Everything else do what the manual states with the recommended fluids. I agree that tractor brand name fluids are a rip off. Just buy that ever the viscosity and govt standard ratings are of what ever you find on sale. If it claims to be SD or whatever certified, it is and use that.
Do not change viscosity of anything, ever. If you follow the factory recommended maintenance schedule, synthetics are a waste of money. After the warranty is over feel free to follow any recommendations any old timer on a message boards tells you. Just remember that real engineers designed your tractor, their jobs are on the line, along with the company reputation.
This applies to tractors, trucks, cars, and airplanes. Anyone tells you different, ask to see their engineering degree and how many units are out there is the world with their name on it.