There can be a very strong lean towards green for the Atari consoles under a modern display, unfortunately. The adjustment for "more red/less green" on the display may need to be quite significant to obtain a palette closer to a CRT; a comparison example has been posted.
The pot inside the 2600 is not a tint/hue control; rather, it adjusts the number of degrees separating the various hues and is highly sensitive. If you own a Harmony cart, the easiest way to set this pot (if misaligned) is to utilize the Color Bar Generation from VideoSoft. The ROM image is attached to this post. Within the first minute or two of powering on a cold (Powered off for at least 45 minutes) console, ensure the bottom border color matches the top border color.
Color Bar Generator.bin 4KB
When the border match is achieved, the degrees of separation is ~25.7, and the Hue 1 range (very closely) matches the Hue 15 range. In turn, the console then is displaying a palette of 120 colors.
Some additional console warm-up will occur thereafter*, resulting in a degrees shift that is slightly greater. Ideally, a setting between ~25.7 and ~27.7 degrees. That setting places Hue 15 between the hues of 1 (Gold) and 2 (Orange), as described in the Stella Programmer's Guide, a 'Light Orange', ultimately providing a 128 colors palette for the console.
*NOTE: This can be observed by continuing to run the Color Bar Generator image, the bottom border will become a darker/richer brown color than the top portion automatically.