Even if you didn't have to sand you still need proper preparation. Oil/grease/dirt/dust are standard on in a build site. Most products require some sort of cleaning (like TSP) prior to working a product. I suggest you search the product (the stain) on line and find out what is proper preparation of the surface prior to applying product.

The "boot print" is some form of oil or wax sitting on the wood that was invisible. A proper cleaning (the day prior so that the wood has time to dry prior to staining) would have eliminated the foot print.

I suggest you stop the application and start talking to flooring professionals and get their approach. I know the theory...I don't know the technique. And a little FYI - protective paper has additives that can transfer to the surface below when you step on it...everything has additives that transfer when you step on them. That's why a proper cleaning would have been the way to start the process. Sanding isn't always needed, but it is ALWAYS a good idea anyway. Even a light sanding goes a long way for wood/floor prep.

My guess is the tread with the boot print will require sanding + reapplication...but get a professional opinion before you do anything else. Staining can be the toughest part of floor refinishing. It can cause the greatest heart ache in the fastest amount of time.