When I bought my lathe [many moons ago ] I bought some Dromus oil from Shell,since this was the stuff we used in the machine shop where I worked. I found,to my surprise,that it stained and indeed rusted my machine. I took the matter up with Shell,but got got nowhere,they could not be bothered. I ended up getting another oil elsewhere which had anti rust built in and never had a problem since..I would not worry too much about a little staining,since the machine is intended to be used,not admired. Rust is a different matter,it,s like an unwelcome guest,it,s very difficult to get rid of,and always leaves it,s mark.
Remember,if your machines are always clean and shiny,you are not making much use of them ! Enjoy them .