to the forum and congratulations on your new Cougar.
There is a drain valve or a pipe with a screw-on cap directly under the tank. The purpose of that valve is to allow you to drain all the water out of your fresh water tank for storage or to winterize your RV. If it is open, you'll experience exactly what you've seen so far. You'll need to access that area and close the valve. If there is skirting around your RV, they should have left an access panel or door so you can get under the RV. Look for that panel, otherwise, disassemble a part of your skirting to gain access.
I'd ask, if you have access to fresh water via a hose, is there a reason you're using the onboard tank and pump? wouldn't it be easier to just hook up water to your city water connection and use the park water for your needs?