Yes, you should have a 30 to 15 amp adapter in your trailer. My 3 way fridge will pop a ground fault interupt if connect to the same outlet as the trailer converter. My fix was to use the 30 to 15 amp adapter on the 3 way fridge which is fused at 15 amps for its protection.
Also, a neighbor may steal you 15 amp connection and you will be forced to use a 30 amp connection. This happened to me in Big Sur. No popped breakers after converting to the 30 amp connection.
In most areas, you may want a 50 to 30 amp adapter.
Make sure you get the correct gender of connections. I made my adapters so they can hang straight down with 90 degree connections so I could close the electricial box in the campground.