Because this is an academy, it does have tuition and fees. They are outlined as: Tuition, per credit hour: $981. Academic Support Fee, per semester: $420. Additional Fees (mandatory):$590 -- (Student Activity: $120, Health Center: $320, Reily Center: $150). Medical Insurance, per academic year: $3,030. Assuming people don't waive the medical insurance, take 16 credit hours (as is the norm for RPI), the yearly cost is: $20,156.
The Provost's Office provides students up to $500 for travel needed to present a poster or paper at a conference. There are other opportunities to be granted money with the purpose of travel for conferences or training opportunities.
Other than this information, I could not find who else would fund this academy. I can assume that Tulane takes on part of the burden as well as governmental agencies in their partner countries.