Tissera was born at Colombo and educated at S. Thomas' College, Mount Lavinia, where, initially appearing in 1954 aged fourteen, he captained the Thomian cricket team in the Royal–Thomian series, known as "The Battle of the Blues", in 1957 and 1958.
He made his first-class debut in March 1959, in the annual Gopalan Trophy encounter between Ceylon and Madras.
[3] He made his two first-class centuries in unofficial Test matches for Ceylon.
[6] A stalwart of Sri Lankan cricket, he managed the national team between 2005 and 2007.
Test matches between West Indies and Sri Lanka are now played for the Sobers-Tissera Trophy, in honour of Tissera and Gary Sobers.