Is a double red cell donation safe?

I recently participated in a double red blood cell donation, as I'm a type O+. But my mom was horrified at the thought of me having my platelets and plasma sent back into my body after they had already been taken out. She calls it unnatural and dangerous because there's no telling what chemicals they use bin separating them, or whether it might be contaminated by someone else's blood. I want to allay her fears, so what's the best way to explain the procedure's safety? Or is there something to her worries after all?