What causes the tingling sensation in a limb, when it has "fallen asleep"?

Sometimes, the tingling sensation isn't because of a loss of circulation, but because the thing pressing against you is pressing, or pinching, a nerve. Pinching that nerve causes interruption of the signals your nerve sends, and that interruption is interpreted as that tingling.

When it is the circulation, it's not stopping the circulation that tingles, but letting the circulation back. The resumed circulation is replumping blood vessels, recirculating through tissue, muscle, and nerves that were deprived. That aches, as you know. Tingling is not the only interpretation that your brain passes on. You can also get cramped muscles and "dented" skin, where the blood takes an extra second or two to fully recirculate in the spot where it was crushed the most.

Its hard to tell without a more detailed history; but it sounds like you might have a pinched nerve. This would be especially evident if you were feeling any burning sensation, excessive sensitivity or a loss of strength in the affected area as well. The symptoms may be due to a bulging vertebral disk(s) on the right side of your spine near the 7th cervical or first thoracic vertebrae. You should start with your regular doctor, but may eventually need to be seen by a neurologist (they also do spine stuff) depending on the extent of presentation.

I would think that as the blood flow returns to the affected area, the nerves respond to the sudden increase in blood.

They probably had been dulled by the lack of blood and the sudden return makes them tingle. That's what I think.

When you foot or arm falls asleep, it means nerve signals aren't getting to your brain, so they get all backed up at the source. When you move your leg or arm, that tingling sensation you get is all of the electrical signals rushing to your brain at once.

The lack of blood and oxygen to the cells,puts the nerves in to alarm mode.Notifies the brain,say to move to reestablish blood flow.

lack of blood flow to the nerve sensory endings.

The beginng of possesion?