Tsai has to send a naval frigate to Taiping island even if she was reluctant to do so because nearly 100% of Taiwan people were very angry with the outcome of the PCA at this moment. And she might lose her new administration to the angry people if she does not do so.
Also this is a military move to prevent Vietnam or Philippines trying to take over Taiping island.
Also there was a rumour if Tsai give up ROC (Taiwan)'s claim on Taiping island because of this arbitration, PLAN might just move in and take over this island.
For people who are ignorant of modern Chinese history, Taiwan is the current site of the Chinese civil war defeated government called Republic of China (ROC), established in 1911.
In 1930s French colonial navy based in Vietnam occupied some islands in South China seas but were expelled by ROC a year later. During world world 2, the islands were occupied by Japan. After Japan's defeat in WW2, ROC sent several destroyers to take over islands in South China sea. Taiping island was so named because a ROC destroyer named Taiping was sent in 1946 to land and take over.
The 9 dotted line was originally called 11 dotted line by Republic of China (which retreated to Taiwan in 1949), but after People's Republic of China (PRC) took over the mainland, and as a good will gesture to the North Vietnam many years later, two of the dotted line near Hanoi and Hainan island was eliminated, and thus 11 dotted line inherited from ROC was changed to 9 dotted lines by PRC.