TL;DR We would like for our replies from Zendesk to be a reply on the tweet we're actually responding to as opposed to the original tweet.

This Zendesk articlementions:

If the ticket was created from a tweet mentioning your Twitter account name (for example @Zendesk), then your reply from within Zendesk will be a reply tweet, threaded to the senders original mention.

We would really like for our replies from Zendesk to be a reply on the tweet we're actually responding to, rather than the senders original mention. We often have conversations on Twitter that go back and forth multiple times, and our responses then end up appearing completely out of order on Twitter. It makes it virtually impossible for somebody to follow along in Twitter itself.

This Community postis along similar lines, but there wasn't a conclusion. For clarity, we are referring to public tweets rather than DMs.

I believe this is a Zendesk limitation rather than a Twitter API limitation, as we haven't had this issue with other platforms we've used to respond to tweets.