You tried it specifically with Quickpic? Or from photos? As slybloty said in his answer it shouldn't do that if you use the gallery app or another local picture app. Try this, download a file explorer like ES File Explorer and go to your DICM/camera folder and manually delete a photo from there. If it still gets removed from your online backup then there must be sync going on on your phone where it keeps the two offline and online the same, although I have no idea what could do that.