Tsa is the seventeenth of the thirty consonants and opens the fifth line. It writes a voiceless unaspirated dental affricate, the ts of English cats, and in modern Lhasa speech it carries high tone. It is a root letter with no prefix, suffix, superscript or subscript role.
Its shape is the shape of ca, the palatal letter that opens the second line, carrying a small added mark called the tsa phru. The same mark on cha gives tsha, and on ja gives dza, so the three affricates of the fifth line are three palatal letters wearing one diacritic.
That is a Tibetan device and not an Indic inheritance. Sanskrit has no ts, so the inherited alphabet supplied no letter for it, and the sounds are ones Tibetan uses constantly. Rather than invent three unrelated shapes or borrow from elsewhere, whoever adapted the script extended what was already there, taking the nearest inherited series and marking it. The economy is characteristic: the script solves its problems by modifying its own letters rather than by acquiring new ones, which is also what the reversed letters do for the retroflexes and what subjoined ha does for the voiced aspirates.
Three letters of the thirty are therefore Tibetan additions in shape as well as in sound.