"When you use a full-attack action to make multiple ranged weapon attacks against the same opponent, total the damage from all hits before applying that opponent’s damage reduction."
I'd say no? It says you add all the damage together, then apply DR. It doesn't seem to consider the possibility that some of your attacks will bypass the DR and not others.
I'd say use the damage from the adamantine bullet separately from the rest.
It just makes things easier.
I agree, I would add up all the damage and apply the DR as per Clustered Shots. The adamantine bullet would all go through, but the use of normal bullets would negate the usefulness of the adamantine bullet.
If the creature had hardness instead of DR, you would apply the full damage from the adamantine bullet and calculate damage for each normal bullet minus the hardness individually, Clustered Shots doesn't help against hardness, just DR.
The way I see it, the feat allows you to shoot arrows/bullets/bolts in a tight formation to overcome DR, it doesn't let you pull off a robin hood arrow in arrow in arrow every time you shoot.
The player was probably trying to do this to lower the cost of using adamantine bullets or more likely adamantine alchemical cartridges (paper). This is where that player should have paid 50g for an oil of abundant ammunition and not worry about shooting all his money into a robot.
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It wouldn't be unreasonable to rule this way in a home game, considering the first shot would conceivably bypass the DR, and the shots to follow enter the wounded area that would seem to have lost it's damage reduction. However there really isn't anything in the feat to say that's what's actually happening, or that's why it works. All it does say is that you add all the damage together then apply DR to the total. Doesn't say anything about one attack bypassing DR causing all attacks to bypass DR. So for PFS, or other types of organized play, I'd say no, and do what the others have suggested. Allow the adamantine bullet to bypass DR, and apply the DR on the other attacks.
The player is thinking the first bullet has to deal with DR and the rest do not, but that is not how the feat works.
He is better off not making or buying anymore adamantine bullets unless he wants to completely bypass DR, and in that case he needs to use them for every attack that round.