Tightening up after stretching means you need to adjust how you approach stretching in general.
This video shows you the WHY and explains WHAT to do about it.
*Special Note for Flexible People*
Remember that if you are already quite flexible, stretching "tight" muscles can make you feel WORSE. If you have good range of motion and you feel unstable after stretching, it's a sign that you need to work on strengthening your muscles more!
This article on When Massage Makes Pain Worse will help you understand why "tight" muscles don't always need to be stretched and loosened!