attaching a coupling to a copper pipe

I am trying to install a standing bottleless water filter in my house and the hoses beneath my sink are incompatible with the adapters that come with my filter. My fridge does not have a water dispenser (which is the other recommended way to connect the filter), but there is a pipe that carries water into the fridge. Although since it neither has an ice machine nor a water dispenser it is effectively doing nothing. .The manual to the fridge explicitly says connecting water to the fridge does nothing if it doesn’t have an ice maker, so I know removing the pipe from the fridge won’t cause any issues on a theoretical level.

Anyway my hope is to be able to connect the 1/4 inch plastic tubing that comes with the filter to this copper tube. I got a 1/4 inch coupling in order to do this, however nothing I do seems to work. Neither the nut, the inner tube, nor the inner compression thing will go around the copper pipe. If I remove the nut from the coupling and use the compressor and the nut already on the pipe, this connects to the central coupling. This seems ok. The issue is when I connect the inner tube, compressor and nut to the plastic tube and screw that into the inner coupling, water just gushes out the side on the plastic tube. Does anyone have any suggestions for me here?

The guys at Home Depot advised me to scrap the entire copper tube and replace it with a plastic one which at the minimum seems like overkill, but they were adamant that nothing else will work. Below is an image of the plastic tube with the nut and inner tube (I have 2 couplings at this point since once I assembled the side with the plastic tube it was impossible to take off and I got an extra coupling). For clarity when I say the water gushes out the side, I believe the inner compressor and the nut is where the leaking water is coming from, not around the seams of the nuts. Water does come out of the end of the plastic tube the way I would want, but obviously due to the leaking this is not a workable situation. I don’t know if there is some kind of glue or magic tape that I can use around the nut to prevent leaking, but that is the kind of advice I am looking for (or if I am doing something fundamentally wrong guidance in the correct direction would also be appreciated).