I have successfully prevented the yellow staining by leaving a wet cloth over the spot after the initial cleaning for 24 hours and replacing it with another clean wet cloth until it stays clean. One of my dogs has to be sick over a carpeted bit. We have hard floors apart from a small piece left under the piano for acoustic reasons and he will run there to be sick!
I have a similar method.
Put loads of cold water on the stain, press down with kitchen towel to soak up most of the water. Wet again and repeat until paper is clean. Don't rub the pile.
I have done above, seems to have worked but think I may have a water stain instead ! Whilst I am cleaning up one load of sick she neatly deposited another one in the other room on the carpet, despite handy tiled conservatory floor ! Was a bit worried as we have had poisonings locally and she did eat something up in the woods. She seems fine now though, wants her dinner !