Should headphones cover the entire ear?

I bought a pair of ONN headphones which fall under the description of full-size headphones:

http://www.techhive.com/article/2000079/infographi...

However, they don't cover my entire ear; my ears do not fit inside them, and instead the cushioning pushes against my ears. I only have worn lightweight headphones and earphones before, so I don't know if this discomfort is a normal thing I should get used to in a week... or if I should get a refund before it's too late.