How To guide on Color Profile?

Hi... I'm new to this processs.. so I may be using improper terms... so looking for guidance to meet my goals.

I'm using Illustrator to design artwork for a keychain tag that I will dye sublimate.

My first print, the colors are 'off'.. e.g., the blue I used is very muted, and the green I used is nearly grey.. the yellow is fine, but the orange/red is more red than orange.

I imagine I need to tweak my colors based on the actual output.. but no idea how to go about that process... is there some calibration process by which I converge on the right colors based on the final ouput on my media?

Any good vids or tutorials on this process?

One other note, in order to get the images into the software I'm using for cutting, I'm exporting the illustrator to a PNG for printing from another software (Cricut Design Space)... what additional caveats do I need to be aware of?

Thanks!