rub (something) into (something)
To use a forceful rubbing action to apply some substance to a surface and cause it to soak or penetrate into it. The doctor told me to rub this salve into the affected area on my face for two to three weeks. I make a point of rubbing this waterproofing conditioner into my leather boots once a week to protect them from the rainy climate here.
rub something into something
and rub something into cause something to penetrate a surface by rubbing it against the surface. Rub this lotion into your muscles. It will stop the aching. Try rubbing in this lotion.