99.99% of the time, when we use the word 'people', it is a plural noun. 'People' means men, women and children, in the plural. We tend to use as the plural form of 'person.'
If you came across an situation in which a native speaker wrote 'that people', there are two explanations:
1. He or she could be using the word 'people', in the singular, to refer to a particular nation or ethnic group. For example, you can say 'The Aztecs were an ancient people who lived in Mexico'. In this sense, 'people' is singular.
2. It could be a mistake or typographical error.