If you're worried about the air exposure, you could always just use a syringe filter. But like many people have said, it's nothing to worry about.
When you draw your oil out of your sterile vial, to you shoot with the same needle? Because if not, you should pull your oil into the barrel and out of the drawing pin as to not waste oil and then put your injection needle on and rid the air of the barrel.
Just another time your sterile oil is exposed to air.
The opening isn't terribly large. An inch around, maybe? If it's really that much of a concern, there's a sterile cap it comes with that you could cover the opening with so it's not sitting there exposed for the few seconds you're messing with your syringe.
Those vials look very small, I can't imagine them holding much more than 5ml, if that. They're also very expensive. For no real benefit over syringe filtering or bottletop filtering, those two reasons alone will deter suppliers from using them.