Cups are fine to use safety-wise, but apparently most women experience incredibly heavy periods the first few menstruating months after giving birth. So heavy that both a tampon and pad are required together, changing to fresh every two to three hours, or just a pad and changing every hour or so. A cup is not suitable for this... hence why I was leaking. I only realised how heavy I was after I started using tampons. *feels a bit stupid now*
So there we go - info for all! :)