As I understand it the reflex is releasing more milk, and creating the hindmilk. She is a Board Certified Lactation Consultant, as well as a retired La Leche League Leader. The function of the let-down, or milk ejection reflex, is to propel your milk to the lactiferous sinuses where it is easily accessed by your baby. This is a contraction of the myoepithelial cells which surround the alveoli, or milk producing cells of the breast. This milk is ejected into the ductules and then moved to the lactiferous sinuses.
Milk typically ejects several times during each feed.
When your baby is put to your breast, prior to your milk letting down, there is some milk available to your baby. As your milk ejects you may notice the frequency of your baby's sucking and swallowing increases as he keeps up with the flow of your milk. If you were expressing your milk, this is the time you would see your milk droplets turn to sprays. Nursing moms don't always feel their milk let down. This may occur during a feed, or in other situations, as you describe - often in response to their baby's cry.