It could be a pH issue, especially if you have sensitive skin or live in a hard water area. Tap water has a neutral pH (about 7) but our skin is more acidic (it varies, but 4ish – 5.5 is normal- slightly higher in men). If you are washing your face with soap or with an alkaline cleanser, this could irritate your skin and make it red. Most soaps don’t have their pH clearly displayed, but can vary from a pH of 9 to a pH14.
Whilst I don’t think water alone would make your face red (unless it is very cold or very hot!), if you are using any sort of cleanser, this could do it. It may be too alkaline for your skin and so your skin becomes a little irritated and temporarily turns red. This is even more likely if you have pale skin or sensitive skin.
The redness goes after a short time as your skin is pretty impressively efficient and will re-balance the pH when the irritant has gone.