Furnace runs with dial set to OFF?

darn mice!lol.

Furnace should not be running if your thermostat is set to "off" - might be time to replace the thermostat - not expensive easy DIY.

Most thermostats have an off switch independent of the temperature control. Picture of your thermostat would help.

Yes it can keep running after the thermostat has been turned off as 425 mentioned till air flow over the heat exchanger cools to a certain temp.
Now if it keeps running and blowing cold air take your 2016 trailer back to a dealer

If it's like the thermostat on my 2000 version, "off" means 45 degrees. When it goes below 45 degrees, the furnace runs.

My furnace has an on-off switch on the front of the unit underneath the grate. I simply turn the furnace off there.

I agree on your BRAND NEW camper, which surely is still under warranty, you should be able to get advice from Palomino and/or a free repair at the RV dealership, if indeed there is a problem.

We have a thermostat acting up,in off position it sometimes turns on. Electrical contact cleaner may help im told,if not will be changing it.

Just to clarify, when you say "off" is there a separate On/Off switch or is it just the temperature setting down to an "Off" label on the gauge? Mine has a separate On/Off switch and in Off it will not run. It will, however, keep running until cooled if turned off while the furnace is running. This tells me it's not an actual power switch but a soft off the furnace can ignore in certain circumstances. Perhaps a little contact cleaner (available at Lowes or Home Depot). Be careful though as contact cleaner can attack some plastics. Test it on a hidden piece of the thermostat to be sure.

..Some thermostats, mechanical, lever just slid to bottom of scale doesn't turn it off. Lever requires a bit of force to continue and actually be in off position. The one that came with our camper felt like was going to break something before it snapped to off position.

Both of my last two trailers were when the dial was set to off it still ran for approximately 3-5 minutes blowing hot air till it came down a few degrees then it shut off and stayed off.

Fan running.......just fan (not heating)

Thermostat not actually OFF........might have to really 'push' lever to off position

Other possibles:
Bad t-stat
Bad wires from t-stat to furnace
Bad 'blower timer' (timed delay relay is a stand alone part/blower timer is part of circuit board)