Large orgs that manage refugee camps tend to have a mix of international and regional staff that have experience working in those types of situations, cultural knowledge of the area and peoples served, and expertise in the functions to operate the camp (including international law, logistics, public health, etc).
The idea of someone being hired in one country with minimal experience and being plucked into a refugee camp to 'help' perpetuates 'white knight/savor behavior in international aid. Not to diminish your experience and travels, but on a practical level large INGOs don't hire folks from with limited professional regional/cultural/language knowledge of a complex humanitarian situation and fly them across the world to work in hardship situations unless that individual has a high level of experience in the area and a track record of working in hardship areas, or is in a specialized field (logistics, epidemiology, etc). The UN tends to give preferential hiring on non-North American/European nationalities.
Refugee camps tend to be the last resort for displaced populations and are actively avoided when possible as they tend to enable/perpetuate the underlying causes while creating new problems. If you're generally interested in the topic and looking to learn more, take a look at the SPHERE guidelines, UNHCR, etc. As well, Emory University has a Coursera course about health and humanitarian emergencies health and humanitarian emergencies. I would suggest also volunteering/working in Canada with refugee populations to start to gain somewhat applicable experience before you jetset across the globe.
The major orgs that do work in refugee/displaced populations: Int'l Federation of Red Cross/Red Crescent, IRC, various UN bodies. They may also 'sub-contract' some functions out to other local/regional NGOs organizations.