Jorge Arenas's page

I agree with Selgard. The text has authority overall.
The text says "..increase the damage die type by one step."

If it were to say "..increase the number of damage die by one step." it would mean to go from 2D6 to 3D6 another example 3D8 to 4D8 and so on.

The two words I'd focus on is "die type", which is referred to type of die used (ie. D4, D6, D8, D10, D12). The increase is consistent using this method. 2D6 would change to 2D8, 2D10 would change to 2D12. For every die you get a +2 max damage increase.

In the case of an Eidolon becoming large by any means I'd would apply the evolutions in order as they are applied to the Eidolon in the the most sensible way.

Eidolon becomes large. Change the base form as necessary for size, add evolutions in order as they can be applied to the Eidolon by prerequisites (ie.Body size, Limbs (to body), Natural Attacks to limbs, then Improvements to Natural Attacks)

So a Large Eidolon with Limbs(Arms), Slam(To Arms) and Improved Damage(To Slam) would go in this progression. From Slam (Large)=2D6 to Improve Damage(to Slam(Large))=2D8.