Unfortunately, on most hot tubs, there is no pressure gauge. So we're relegated to cleaning on a regular pattern. If your system is pressurized and has a pressure gauge, then you could certainly go that route as well.
I've seen some of these newer tub filters being made out of polymer and the dishwasher being the standard way of cleaning them.
But, if they are standard fiber cartridge filters, then I'd suggest you rinse them with a hose every couple of weeks and soak them with a good cartridge filter cleaner (see your dealer or online hot tub chemical store) when you do water changes. I rotate 2 sets of filters so I can put a clean set in as soon as I fill the tub up. Then I soak, rinse, and store my dirty set. Always worked well for me.
Is what your dealer recommended wrong? Hard to say. Maybe he wants you to tear up filters faster so you come in to buy more? You could contact the manufacturer and ask how they recommend doing it...