Rhaphidophora tetrasperma is only distantly related to Monstera and Philodendron. It is from almost the other side of the world in SW asia, the others are from central and south america. Grow it in a good moist but not wet loose fast draining grow mix, Something like 50% - 60% shredded bark or pumice, with the rest equal parts peat and compost with a little charcoal tossed in, mix it all well and don't pack it down into the pot. Alot of folks here would recommend Turface but I've never used it so I can't give an opinion of it but I've been in the research greenhouses at MOBOT in St. Louis and they use a similar mix there and some of the plants grow in it for years. Than give it something to climb cuz it'll want to climb if you give it good growing conditions. By giving it a pole to climb it will attach its roots to that rather than something like a table leg or the molding around your windows. If you get roots that just stick out in the air you can either guide them as they get longer back into the potting mix to aid in feeding the upper portions of the plant, leave them to hang loosely or just cut them off. Ideally, humidity should be on the higher end of things but like most house plants it should be able to adapt somewhat to home conditions, Just don't let it dry out. I have for the last couple of years ran a humidifier and it makes a huge difference to both my plants and how I feel during the winter. Check out the link below for more info, it is not my site or a commercial site. Here is a link that might be useful: Rhaphidophora tetrasperma

Drop me a private note and I'll give you a cutting. I can't offer this to a bunch of people since my plant is only about 6 feet tall but I don't mind giving away one or two. No charge, just pay the postage. Steve Lucas You can find my email address at the bottom of the page on this link. Here is a link that might be useful: Exotic Rainforest

By the looks of it, I'm pretty sure you can rule out under watering and too much sun as possible reasons. Whatever the case, I'd hold off on fertilizing it until the plant recovers.

The plant look like it needs to be in a bigger pot. When you took the plant out of the pot, was there more roots than soil? It looks like the water could be running down the side of the pot instead of the root ball. I think you are watering too much. I have four RT‘s all growing nicely. I use a tell to know when to water. A wooden stick inserted into the pot reaching the bottom. If it is dry when i pull it out than I water. As long as your plant is not in direct sunlight, the light is fine. Mine don’t receive that strong of light. I hope this help. Ellen