This is due to Vasolidation - widening of blood vessels, which occurs during massage. Nitric oxide found in our blood relaxes the inner walls of the blood vessels, allowing them to expand. Hence blood circulation is improved. You will notice that your skin looked flushed and slightly pink.
Sometimes vasolidation may trigger the release of histamines too which caused the itch to occur. Histamines are our body's defence mechanisms against foreign particles. The itching effect may last up to 10 minutes. Most often, the itch triggered by massage is harmless. The itch may be mistaken as allergic reaction to the skincare used during a facial massage.
If the itch and redness continues for more than 10 minutes and do not seem to subside, your skin may be experiencing some allergic reaction. Every skin reacts differently and you know best what is happening.
A facial massage is beneficial for everyone as it promotes blood circulation. Do not let a little harmless itch prevents you from enjoying the benefits of a facial massage.