In the next turn, we get mud so it's impossible for me to break them free. But, I took the added step on the clear turn of putting two airbases in the pocket and loading up two airbases outside the pocket with transports.
On the mud turn, I flew in enough supplies that all but two units had airhead supply. They went from red to orange supply status.
Now I get the turn back and everyone surrendered. What just happened here? [&:][&:][&:][&:][&:]

The rule as it is supposed to work:
v1.05.18 - September 6, 2011
Airhead supply. Isolated air units may be changed to beach/air supply status (same as old beachhead status) under certain conditions. If a player flies in supplies to an air base in a pocket, the supplies will immediately be distributed amongst all of the isolated units that can trace to the air base. If the amount received during the turn at some point equals 5% or more of the total needs of the unit, then the unit will be immediately set to beach/air supply status (it will display in orange instead of red when toggle unsupplied units is toggled on). The total needs are the supply+fuel+ammo needs listed for the unit. So a division with total needs of 1100 tons of s/f/a have at least 55 tons flown in and delivered to the unit, it will have its supply status changed from isolated to beach/air supply status. This will last until the next friendly logistics phase. Units with beach/air supply will always pay penalties for being short of ammo, so there is a disadvantage in combat to be in beach/air supply (but it's better than being isolated where there are additional penalties). The air base must be in a clear or light woods hex. When in Beach/Air supply, the unit detail screen will show the information: Air Head Supply 400 / 20 (5%) which indicates the total amount of supplies+fuel+ammo the unit needs, the amount it has received via air resupply, and the total percentage of needs that has been met. When in Air Transport mode, the player can left click on an air base and then bring up that unit's detail screen to see a full list of all isolated unit that can trace to the air base, the total need of each unit, and the amount of supplies that have been sent to the unit. On the right side of that screen is a line that reads Air Supply Range: 10. By clicking on this line, the player may enter a different number from 1 to 10. Only units within the state range in hexes of the air base will be sent supplies that are airlifted to this air base. Air base units may be moved before supplies are delivered to it, but once it receives supplies for isolated units, it will not be able to move and then receive additional supplies for isolated units. Units that are merged or divided track the amount of air head supplies received, so they can lose their supplied status if no longer over the 5% threshold. The Soviet player may not fly airhead supply on the first turn of any scenario starting in June 1941.
Units in beachhead/Air head supply will not suffer more than a 33% reduction in CV due to supply shortages (used to be it could be up to a 75% reduction in CV).