Yeah, pretty much this. The portal starts out subatomic (essentially point-like, or as much as quantum physics might allow anyway), and then is grown up to its desired size, shunting whatever's caught on its surface to the other side as it grows. Stuff (hopefully just air molecules, but who knows) would cross back and forth repeatedly as the portal catches up to it during growth stage.
As for the inside of the portal, as I understand it, it literally does not exist anywhere at all. The portal is just a continuity between two regions of spacetime. The sphere-shaped region that should be inside of it is just something like a defect on the structure of spacetime that exists as long as the portal does. There is no space there, so any question along the lines of "what does it look like in there" has no possible answer at all.