I always lay down for glute injections. Much easier than standing in my opinion.
Also, if you squeeze a little of oil out when you're getting the air out of the syringe, the oil runs down the outside of needle and pools at the bottom. Some of the oil you're seeing on your glutes, may be that oil running down the outside of the needle onto your skin. Just a thought. You may not see this with every injection site due to the angle at which you hold the needle.