Tigress' serious personality as an adult was partly the result her years as a youth with Shifu. During training, if Tigress did something wrong, she would be scolded or be pointed out of her mistakes in an unkind way; something right, she would be given a look of contention (not happiness) from Shifu. Shifu was scared that if he were to be very emotionally supportive to Tigress, she would turn into another Tai Lung.
The other partial contribution to Tigress' serious personality, which was greatly expressed when Po was chosen as the Dragon Warrior, can be seen in the Secrets of the Scroll.
For most of that short movie, Shifu has been trying to turn Tigress into another version of himself by teaching her his fighting stance and his kung fu skills. Eventually, Shifu learns that Tigress and the Four would be better fighters if they went with their own style of kung fu. But just because Shifu isn't familiar with these five kung fu styles, it doesn't mean he is useless. He applies his personal philosophy of strict control/perfection on the Five to improve their kung fu style.
Now the years go by until KFP1 begins.
The Five have their individual personalities intact, but they're more strict and less talkative due to Shifu's teaching methods. When Po is chosen as the Dragon Warrior, the Five are angry because their years of hard work goes unrewarded. But Tigress takes the longest to warm up to Po possibly because she had Shifu as a (surrogate) parent and a teacher a lot longer than the Four.