When you plug into 120v AC the camper automatically switches over to the Converter power as a source of DC, of course…
The converter will put out 13.xx to 14 volts, and you notice the lights get brighter as compared to the battery. The converter is charging the battery so needs to have a slightly higher voltage than the battery has. This is not a "spike" and should be perfectly fine and good with all DC appliances and devices.
It is odd that you are blowing your phone charger, is your charger a really cheap one? $3? Maybe the solution is to get a better phone charger. A charger should be able to handle 13 or 14 volts easily, your truck will be making up to 14 volts through the alternator (usually in the 13.xx range as your camper converter), so the phone charger surely is made for this similar voltage.
You pulled 12v positive off the light, where did you ground it? Although I have done the same and pulled 12+ from one side of the light and 12- from the other and everything played well together…
You could wire your DC outlet to run off the battery only, but that is more work to run wires and fuses than just tapping into existing wiring.
I would first try another charger before moving forward