All Teflon pans are non-stick, but not all non-stick pans are Teflon ;-)
Teflon, when new, is one of the slippiest substances known to man. Nothing will adhere to it, not even oil. When new, you can have a hard time getting an even coating of oil unless you make it deep enough to fill a base layer. The oil will be more attracted to itself than to the pan.
Once you've been frying in Teflon for a few months, the surface gradually does begin to get coated in carbon, from burnt ingredients &/or oil. I don't know quite what causes this - potentially the surface getting slightly damaged or roughened by abrasion; but an older Teflon pan will more easily coat in an even layer of oil.
If it pools in patches, then the best reason I can think is that some areas are more abraded than others, or the pan base may be going out of true. Most cheap frying pans will eventually bow one way or the other over time - some forming a 'moat' round the edges as the base has bowed inwards, others a 'pond' in the middle, as it bowed outwards.
A 'quick fix' for cheap pans affected in this manner is to put it [cold & clean] on a carpeted floor & gently stand in it. It's a bit rough & ready but it's not worth fixing professionally.
From comments - The Frying Pan Ballet Company…
[credit David Hoffman + 10 mins in Photoshop by yours truly]