If anything a catalytic heater, by nature of being a lot more efficient that combustion, produces more water than combustion does. But make no mistake, the reaction is still C3H8 + 5O2 -> 3CO2 + 4H2O. Just with the Platinum catalyst in there. But it's still 4H2O coming out.
If you're not ending up with an overly humid environment, then you either have a very leaky tent/camper/whatever or some sort of exhaust setup like camper vans do. Would also help if you live in an area of low relative humidity to start with.