When does Fog of War begin?

[Shad]

The rule as written:

After both players have conducted three activation segments each, then each player rolls three dice at the end of each of his subsequent activation segments. If he rolls 16 or more, the turn ends immediately for both players, and nobody may take any further actions that turn (including recovering morale for unactivated demoralized units). Proceed to the next turn. Add a +1 modifier to the Fog of War dieroll on night turns.

The way I've always played:

A1-B1-A2-B2-A3-B3-roll FoW-A4-roll FoW-B4 etc...

The way campsawyer plays:

A1-B1-A2-B2-A3-B3-A4-roll FoW-B4 etc...

Alan's logic hinges on the phrase "subsequent activation segments", arguing that subsequent after 3 = the fourth.

I don't have any logic. I just have always played end of 3 begins Fog of War.

Curious how everyone else plays this, and how everyone else parses the rule.