That depends on what you are cleaning it with. Some cleaners do not worry about coffee stains or length of time, and some cleaners prefer the stain dry first. So, it matters depending on whether it was Scotch-Guarded and whether it is on suede or velvet or cotton or silk and it matters what you are cleaning it with.
The quicker the better. Milk smells and breeds bacteria and fungus. If it's allowed to soak deep down then there's no chance to clean it up properly. If there's no milk in the drinks, then the quicker the better still works to reduce the stains.
I don't know what DMSO is. My bottom level is hardwood but my stairs and upstairs bedrooms are carpet. It's new so I haven't had any cleaning situations yet, other than regular vacuuming. I just checked to see what DMSO is, and no I've never used solvents on my carpet except for one time when I was living in an apartment I used duct tape to hold an extension cord in place and the sticky got on the carpet. I had a mess but using a solvent/Resolve/solvent/Resolve over a few days finally got it off.