I put a Rig on an offshore oilfield. The oil started depleting instantly, as if there was some internal buffer on the rig, which there is NOT. Although i havent taken measurements, I actually think the available oil drops FASTER when there's not a tanker there to be pumped into.

i am assuming you're playing the experimental 18.x branch of factorio with the latest version of this mod?
actually there is an internal buffer to the oil rig. it is configurable through the mod settings, and if you'd prefer to play with (almost) no internal buffer, its possible to set the value to 1 or another low value.
When selecting an oil rig (selecting it, not just hovering over the entity) a seperate gui element should pop up in the upper left corner, informing you about the status off the internal storage of the oil rig.

AHA! I hadn't noticed that GUI element up in the left corner.

Thank You! I rescind my bug report, this all makes sense. Working as intended!