Damage reduction applies to the total damage of the attack, which includes things like sneak attack damage and critical damage. The damage isn't applied sequentially.
What Are said. When you make a successful attack, you roll your damage. All your damage. Then damage reduction is taken off the total. DR is meant as exactly that, damage reduction, not a way to defeat sneak attacks or critical hits.
DR is applied to the total damage for each attack.
however a dm can do what ever he wants even if its incorrect
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There was a rule in 3.5, if I am remembering correctly, that stated exactly what you GM is ruling. If your normal attack did not penetrate the DR and deal at least one point of damage, precision damage was not applied. This rule was removed in the conversion to Pathfinder and thus, by RAW, no longer applicable.
There was a rule in 3.5, if I am remembering correctly, that stated exactly what you GM is ruling.
This is not the case. The 3.5 rules are the same as the Pathfinder rules in this aspect.
These two examples from the 3.5 FAQ illustrate this, despite not addressing that particular question directly:
For example, if you have a Strength score of 16 and you hit an iron golem with a +1 construct bane longsword, you’ll deal 1d8 +1 (base damage from the +1 sword) +2 (extra enhancement bonus against your designated foe from the bane property) + 3 (Strength bonus) + 2d6 (bonus damage against your designated foe). On average you’ll deal 17 or 18 points of damage to the golem, which is enough to get a few points of damage past the golem’s damage reduction of 15/adamantine.
If the maneuver or stance simply adds to the damage dealt by the attack, add that damage before applying damage reduction (which might in turn reduce or even negate that extra damage). For example, a character in the Punishing Stance adds +1d6 to damage rolls with melee attacks. If you hit a creature with DR 10/— with attack that deals 8 points of damage and an extra 3 points from Punishing Stance, that creature would take 1 point of damage.
There was a rule in 3.5, if I am remembering correctly, that stated exactly what you GM is ruling. If your normal attack did not penetrate the DR and deal at least one point of damage, precision damage was not applied. This rule was removed in the conversion to Pathfinder and thus, by RAW, no longer applicable.
The rule you were thinking of was for things like poison.
Whenever damage reduction completely negates the damage from an attack, it also negates most special effects that accompany the attack, such as injury type poison, a monk’s stunning, and injury type disease. Damage reduction does not negate touch attacks, energy damage dealt along with an attack, or energy drains. Nor does it affect poisons or diseases delivered by inhalation, ingestion, or contact.
Fair enough. I only played a few games of 3.5 before switching to Pathfinder (though I did a lot of 3.5 theory crafting). I stand corrected.