"The boy drinks his tea."
Translation:Pojken dricker sitt te.
No, sitt doesn't imply that he made it himself, only that it's his. But sin te would emphasize that you're talking about a serving, like 'one tea' in English. Saying that would be much less common. With öl, we use en öl, min öl 'a beer, my beer' etc all the time, but it's less common with tea and coffee.
Yes, "The boy drinks his tea" could be translated in Swedish by either "Pojken dricker sin te" or "Pojken dricker hans te". But they mean different things. It depends on whether the tea belongs to the boy who is drinking it, or rather to his dad, or to the guy next to him, or something. In English we don't specify, we use the same possessive pronoun for both meanings and use context to clarify who's tea we are talking about.
There's already comments above explaining that. "sitt" or "hans" is used here to mean "his" tea. That's called 3rd-person masculine possessive. Er/er/era would be 2nd-person plural possessive and so has nothing to do with this exercise where we are dealing only with 3rd-person. (A 3rd-person pronoun refers to someone you are not talking to; you are talking about them to someone else).
All three are 3rd-person reflexive possessive personal pronouns. This means they are only used if the tea being drunk belongs to the drinker and the drinker is not the speaker or listener.
The difference is that sina is for plural objects. "Pojken dricker sina teer" could be used if he is drinking more than one of his own teas.
Sin is for if the singular object is of the common gender, while sitt is for neuter gender singular objects; this is the same as the distinction between en & ett. This means you would say sitt hus, but sin katt. Te is a special case. You can say either sitt te or sin te; this is because sin te is actually short for sin kopp te, just like English "a tea" might be considered short for "a cup of tea" (similar shorthand is used for "a beer" or "a coffee" to refer to a single serving of an otherwise uncountable use of a noun).