Ti-saranam gacchami means that one abides by the Three Gems with one’s heart and soul. Those who have gone to and relied on the Three Gems are Buddhists.
Were There Many People Who Came and Followed the Buddha During His Lifetime?
Yes. On the way from Sarnath to Magadha State after the Buddha’s first sermon, many people were converted to follow his teachings. Among them were three brothers, Brahmins, by the name of Kassapa. They had been Zoroastrians, but were now converted and brought along with them more than one thousand of their followers to be converted to Buddhism. After the Buddha arrived in Rajagaha, the capital of Magadha, many more people were converted, including some who were to become prominent disciples, like Sariputta, Mahamoggallana and Mahakassapa. Afterwards, when the Buddha returned to his native land, a number of his relatives:his younger half brother Nanda, his cousins Ananda and Devadatta, his son Rahula became monastic disciples. Among them, there was a barber named Upali, who had served the royal family, and later became a famous master of Buddhist disciplines (Vinaya bhanaka). The Buddha’s aunt Prajapati also followed to become the first female monastic disciples of the Buddha. Besides, even more devotees were converted to the faith without renouncing the home life. Therefore, the Buddha’s disciples consist of Bhikkhu (monks) and Bhikkhuni (nuns), who form the Buddhist monastic order; and Upasika, who are the male and female lay followers; together they are known as the four groups of disciples. (From Essentials of Buddhism: Questions and Answers)