When alpha hemolysis (α-hemolysis) is present, the agar under the colony is dark and greenish. Streptococcus pneumoniae and a group of oral streptococci (Streptococcus viridans or viridans streptococci) display alpha hemolysis. This is sometimes called green hemolysis because of the color change in the agar. Other synonymous terms are incomplete hemolysis and partial hemolysis. Alpha hemolysis is caused by hydrogen peroxide produced by the bacterium, oxidizing hemoglobin to green methemoglobin.
From this it seems that in alpha hemolysis , it's not the lysis that's the defining event rather the chemical change of the hemoglobin molecule.
Beta hemolysis (β-hemolysis), sometimes called complete hemolysis, is a complete lysis of red cells in the media around and under the colonies: the area appears lightened (yellow) and transparent.
I am unsure of the reason for color change (blood agar plate) in beta hemolysis, my guess it's due to diffusion as I have found no mention of chemical change in hemoglobin molecule anywhere (yet). So far my position is chemical change in hemoglobin without lysis is alpha hemolysis and lysis followed by diffusion of the hemoglobin molecule is beta hemolysis. Problem is my support is shaky at best.