It's the nature of the ink. The pigment carrier is mostly water. But water alone won't do what needs to be done to prevent clogging of the print heads, etc. So, they add various glycols and glycerines. As noted in a previous post, at room temperatures these additives have very low vapor pressures and thus make the transition from liquid to vapor very slowly.
The idea that somehow a sheet of paper over the print is going to "absorb" these compounds is, well, laughable. Not going to help, as you have found out.
The only things that help speed the process of driving off these compounds are heat, and air movement. Heat to supply the energy to make the phase change from liquid to vapor, and air movement to blow the vapor away from the print so it doesn't just reabsorb what you are trying to get rid of.
One way to accomplish this (and there are doubtless many methods that will work) is with a hand held hair dryer. Low heat, high fan. Hold the dryer in one hand and support the print with the other. The hand holding the print can feel the changes -- at first the print will get slightly colder and feel damp, then it will experience a rapid warm up. When this happens, move to another area of the print. Repeat until done. BTW, you can smell the glycols coming off the print so there's no doubt what's happening.
Using this hair dryer method I've gone from printer to framed and on the wall in 45 minutes. These prints don't out-gas. Even in the sun. Even the black areas.
OTOH, I've got a large print on Photorag (cotton rag matte surface) that still out-gasses after five years. I'm just too lazy to a) move it to a location where it gets zero sun, or b) to tear down the framing and process the print to get the contaminates out, or c) interrupt this "experiment" to see what bad things happen to the print over the long term because of the out-gassing (so far, nothing at all visible).
Finally, I've had prints, again on HPR, that were in the frames out-gassing, that I've gone through the trouble of tearing down the frame, drying the print, and reframing. Every time I've done this it's solved the out-gassing problem. So I know it works.