As you can see from the pdf Lelandstanford posted adjusting this valve requires a few special tools that most people don't have. I have a set of gauges, the main tool to do this but I will tell you I have never checked mine and here is why. After a good 10 mile drive to my job which is mostly down hill to the Maim River Valley the rear brake drum generate a good deal of heat as compared to the fronts. I checked this a while ago so I can't tell you the exact difference as I used a pyrometer. The thing is that the backs should be running cooler then the fronts but should be generating some heat. This is with an unloaded truck.
If the back seem to not produce much heat at all then they are likely not working. The other thing to consider is this, I need to adjust the rears about twice a year to keep a good pedal. Now this can vary a great deal depending on driving habit but the thing is, this stays consistent to the driving I do. If this were to change I would suspect a problem. Something to keep in mine.
The other thing to consider is too much pressure getting to the rears. If the rear drums get hotter then the fronts this would be a concern. You would likely notice along with this the back brakes locking up easily or if you have ABS, it activating very easily in wet conditions. I don't have ABS and run Bridgestone tires, the back do not lock up easily. The reason I throw tires in to the equation is that tire adhesion is a big factory to consider when your trying to determine brake lock up points. The first change I made to my brakes were better tires. The BFG that came on it were terrible in the rain, take off or stopping.
As far as you brake history goes this is basically what I figured, you just got the truck. I'm sure you read about all the possible causes, plus we can't yet rule out the rear brake drums. They are well known for causing brake shutter. I have found you can get a good indictor of drum problem while adjusting the rears. If the brakes get tight and then loosen as you spin the wheel you likely have warped drums.
As far as the fronts go, just make sure the hubs are clean. You might want to look at this:
How To: Early Tundra Brake Upgrade
Even through this is about doing the upgrade I threw in some very good advice on installing pads and rotors.
Did Hawk send you a bed in procedure? Is so skip it, just drive normally and avoid any hard stops. Bed in procedures are for race cars.
Mike