The feat states it improves the damage die type by one step. That is what it does. So, 1d8 becomes 1d10.
The creature may add a feat in the order most beneficial to them. This was in the 3.5 FAQ under the practiced spellcaster feat. Therefore, you can decide which order you want to apply the feats for the greatest benefit.
For 1d8 if you apply Improved Damage then INA, you get 1d8 -> 1d10 -> 2d8.
For 1d8 if you apply INA then Improved Damage, you get 1d8 -> 2d6 -> 2d8.
For 1d6 if you apply Improved Damage then INA, you get 1d6 -> 1d8 -> 2d6.
For 1d6 if you apply INA then Improved Damage, you get 1d6 -> 1d8 -> 1d10.
Most of the time, it is pretty close.
Improved Damage states it works on "one natural attack form" but at the end of the description, it states "Each time an eidolon selects this evolution, it applies to a different natural attack." I'd say this is ambiguous. To me, I'd go with one form like claws, so if you have 4 claw attacks, it would apply to all of them.