I'm not sure which hack Tweetbot is using to do this (I think search as noted below), but you can tell it's a hack because it only works for recent-ish tweets. If you go to a tweet a couple weeks old and view details, you can see that it won't fill in the replies.
The way clients usually do this is by fetching all mentions to the user after a given timestamp (of the original tweet), and collecting only those that are replies to the tweet. Since there's a limit on how many mentions you can get, you might not get all the replies.
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I'm not sure which hack Tweetbot is using to do this (I think search as noted below), but you can tell it's a hack because it only works for recent-ish tweets. If you go to a tweet a couple weeks old and view details, you can see that it won't fill in the replies.
Can confirm, Tweetbot never has "all" the replies.
The way clients usually do this is by fetching all mentions to the user after a given timestamp (of the original tweet), and collecting only those that are replies to the tweet. Since there's a limit on how many mentions you can get, you might not get all the replies.
It's been like that at least since 2013.