"As a junior chrononaut, you mustn't interact with your past self under any circumstances, as this will destroy the universe. On the bright side, you don't have to memorize every historical date, since your temporal tablet has a built-in search engine."

Mustn't means "do not do this." Interacting with your past self is forbidden because it has disastrous consequences.

Don't have to means "it is not required." You aren't forced to memorize the dates because the tablet does the work for you.