Relationship between air press and turbo

No relationship at all, other than they are both measured in psi. Not all trucks have a pressure gauge for the turbo boost.
At idle the truck is sucking in air pretty much like your car. As you give it more throttle the exhaust gases flow more hot air through the vanes of the turbo charger causing it to spin faster causing the compressor side of the turbo to start ramming the intake air into the engine at an ever increasing pressure. This pressure is measured in psi.

 

The relationship is that the compressor gets it's air from the intake. The boosted air helps the air compressor not work as hard. You can see the hose go from the intake to the back side of the compressor.

 

many trucks see a 1-2psi drop in turbo boost when building air as the air compressor draws its intake air in from the intake manifold so it is taking some of the cfm from the turbo to compress your air tanks.