No. The geometric center of a (symmetric) lens focused at infinity is the distance f from the film plane measured on the central axis of the lens. When you add an extension tube of thickness t, you’re simply moving the lens forward by t.

This is precisely the same as displacing a lens forward by extending the bellows. The exposure calculations are the same for an SLR with extension tubes or a view camera with bellows extended.

I wonder if the manual you referred to presumes a REVERSED lens. Many SLR makers recommend reversing the lens to optimize image quality at very close focusing distances because of the retrofocus design made necessary to provide the clearance for the swinging reflex mirror.

That could position the center of the lens at a different point and result in a different calculated result.