Cleaning coated gear in general: cool~lukewarm water, minimize wet time and avoid soaking as much as possible. Use a "sport wash" like Atsko or Nikwax only if needed. Air dry and NEVER use heat. Hang in the shade if possible when outdoors. Less is more!
I let the item hang to let most of the water drip off and aid drying by wiping with a towel, just like you got out of the shower. That speeds drying and lets you dry the inevitable features that trap water. I let my pack drip upside down, towel it off and then right side up to let the stuff evaporate out of the innards. A dry towel will wick a lot of water out of 3D foam padding on the straps and back panel and really speed drying time.
With a tent, a few stains are just a badge of honor, but I like to get the loose stuff off. Decomposing needles and other debris are rot traps, so they have to go. I like to rinse the perspiration out of my pack suspension when I get home– just a good rinse without soap, using a sink sprayer in the laundry tub and hang dry.
You want it all bone dry before storing. I prefer to store coated items loose for long term storage, hoping to avoid mildew, odors, rot and sticky coatings.