I have a Seneca but it may be plumbed similarly to yours. It does not have a gravity tank fill like my older units, all water has to enter through the hose connection at the panel.
If I fill the tank using pressure from a hose ("City Fill" on my panel) it goes through the onboard filter and then into the freshwater tank. So all water I put into the tank gets filtered on the way in. If am using City water directly it also passes through the filter before going to the fixtures. When using the tank and the pump, it does not pass through the big filter again.
Might be how yours works if Jayco is consistent between lines of RVs.
2014 Seneca 37TS
Toads: 2014 Ford Explorer Sport or 2013 Ford Focus ST