"Low carbon dioxide levels lead to narrowing of the blood vessels that supply blood to the brain. This reduction in blood supply to the brain leads to symptoms like lightheadedness and tingling in the fingers. Severe hyperventilation can lead to loss of consciousness. For some people, hyperventilation is rare."

I understand the tingling of the fingers to be caused by a reduction of calcium ionization:

"Low levels of carbon dioxide cause tetany by altering the albumin binding of calcium such that the ionized (physiologically influencing) fraction of calcium is reduced; one common reason for low carbon dioxide levels is hyperventilation."