So looking at this on the Jayco site, it appears to have split AC/Heat (separate systems) with the standard mercury switch T-stat for the heat (evident in the current year pictures). That generally indicates non-ducted A/C with ceiling discharge only.
When you say the heat is off, is the switch off (my experience with these is that the on/off switch is VERY stiff and hard to move), or are you just turning it "all the way down"? Note that full down is not actually that cold, so if the AC got it cool enough, it would call for heat.
Have you changed out the original T-stat for a better one? Some residential T-stats have a minimum temp setting and will call for heat below a certain setting regardless of switch to prevent pipe freezing - off on these is more like a vacation setting.
Was it getting fairly cold in the TT when the heat kicked in? Low cool can still get the unit pretty darn cold, it just takes longer to get there than hi cool.
2011 Jayco X19H (purchased 2015)
2008 Jayco 1007 PUP (purchased new, traded for the X19)
2018 Nissan Titan Midnight Ed.