The angry or sorrow will let people feel uneasy, hard to sleep even twitches. That just because the over exciting and angry will make the nerves system disordered, the disorder nerves will make the muscle contracts especially the sensitive organ or partial of your face. The eyes are the most sensitive organ in your face, so it twitches and it's normal. Please relax after the deep breath, drink some water to pacify the mood. If something happen, just let it be. Because the angry will make your whole body disorder and risk the health such as inducing the angina and myocardial infarction. They are dangerous! Take care of yourself!
It is not normal. When you get angry, the emotion is high which may be stimulated with coming invisible bacterium which will cause your eyes infection. The eyes infection will cause your eyes twitches. You'd better use the eyes drops with anti-inflammation to make your eyes keep healthy. You should keep the good mood every day which will be so important for your health of the whole body.