Color issue with PS

Below is a demo of how this can work. I photographed a scene under low quality, unbalanced lighting. But a color checker chart is in the scene, so in any good photo editor (Photoshop is shown), there should be a tool that will color-balance the image based on an area in the scene that’s supposed to be dead neutral. That’s the purpose of the gray patches on the chart, to be a calibrated neutral reference. In the demo example, one click of the gray sampler on a gray chart patch gets most of the way there, but some manual tweaks will still be needed because the light source was so bad. If the lighting was studio quality, it might be close to perfect after clicking the gray square.

If you shoot in raw, for higher quality this should be done in a raw processor such as Adobe Camera Raw or Lightroom.

You don’t have to put the color checker in every picture, but to achieve that, you must enforce consistency. The white balance in the color checker image is valid only under the specific lighting conditions in that shot, so as long as both the lighting and camera settings are locked down so that they’re held constant for all photos (not allowed to auto-adjust), you could in theory apply the same white balance to all of the images and you should be fine. But for color-critical images, maybe take an alternate shot with the chart in it and apply the same correction to the shot without the chart in it.

If you look closely at pictures of space probes like the Mars landers, they use the same type of tool: They attach a calibrated color checker chart to the vehicle in view of at least one of its cameras, so that they can calibrate their pictures and know when an image is showing actual, corrected colors of Mars.

Calibrating Mars
Two Colorful Calibration Targets Will Help Scientists Measure Martian Scenes

https://www.planetary.org/articles/calibrating-mars

You need to process your raw files to get a good visual match. That's necessary no matter which raw processor you use. You can't expect any automatic process to fix this.

Start with good neutral and even lighting! That's the most important thing of all. Include one of these in the shot, so that you have a reference. The color patches have standardized values (although you will mostly use the neutral patches to get the gray balance and tone curve right). You may still need to tweak individual colors and tones until it looks right:

All of this is still rather uncertain until you have a calibrated and profiled monitor, so that your file is correctly represented on screen:

At this point, you're over the hurdle. From here on in, there are standard color management procedures to preserve the colors downstream to final output.