Hi JK1,
I may be able to help. I have restored many water-roof-damaged campers and can pass along some of what I have seen and found when doing roof repairs.
A few things, you called your roof to be a rubber roof. Sadly, the RV industry stopped using actual EPDM rubber a number of years ago. TPO and PVC membranes are now very common for travel trailers. Both are a plastic formulation, no rubber at all. This link to the Coleman site states the Lantern model uses a TPO membrane on a 3/8" decked full walk on arched roof. https://www.dutchmen.com/product/coleman-lantern#constructionOption If you have something other then the what I found, please tell us what it is you have.
The pooling or ponding as many roofers call it, can be a long term problem depending where the ponding is occurring and if it constantly ponds in the same spot. Repetitive ponding happens when the decking has sagged and there is a low spot when the camper is setup level or even nose up or down sometimes. Left over dirt and mold as time goes on will create a discoloration in the ponding area. The water evaporates and what is left is the mold/dirt etc. concentrated in that area. The actual membrane can withstand the ponding in it's virgin form, however any caulking/roof sealants that are under water during ponding can be a problem over time.
Can you post a few pics of the roof showing the discoloration and where it is located in relation to any roof seams? It is easier to talk to what you are seeing then just generic answers.
I hope this helps.
John