Conversation so far:
How were the Sinhalese kingdoms formed?
Sinhalese kingoms were formed by Prince Vijaya and his 700 followers. They left Suppāraka, landed on the island and founded the Kingdom of Tambapanni.
Who or what are the Tambapanni in relation to the Sinhalese people and their kingdom?
Vijaya claimed Tambapanni his capital and soon the whole island come under this name. Tambapanni was originally inhabited and governed by Yakkhas, having their capital at Sirīsavatthu
Is Tambapanni where the Sinhalese live today?
Who is Vijaya in relation to the Sinhalese people?
Prince Vijaya was the traditional first Sinhalese king of Sri Lanka

Question: Did he take over the Sinhalese people?
Self-contained rewrite: Did Prince Vijaya take over the Sinhalese people?