Every magnifying glass I've ever messed with gives me the same results regardless of which side I'm looking at. What creates a difference between the object being enlarged and my eye, and a focused spot of sunlight that burns and the sun itself, is the varied distance of the enlarged object/burning point and my eye/sun.
Now if someone has a magnifying glass that behaves completely different by simply turning it around, perhaps they could post a picture of it. Video would be great. Maybe an online source and description?