Use spot color file to fix a seperate file?

Hello, I have 2 AI file, they are the same artwork but different in color: one have full color with CYMK mode and one look like a B&W but still in CMYK mode (supposed to be the spot color file). I exported the AI color file to PSD with the same CMYK mode to do some logo design then sent to my client. They feedbacked that the color looks weird and asked me to use the sot color file to fix it. I've no idea how to use it because - it looks like a B&W file. Both AI file has some color setting look like this one:

https://drive.google.com/file/d/1edHpiqhAdMGnrFAd5OXCZBObv8Zsde_0/view?usp=sharing

Can someone help how I to fix it please.