Side Conversation Replies from Customer Not Threading; Creating new Ticket

We have a customer that we email with regularly and they work out of Salesforce for their communications. For a long time, their replies to our tickets would not thread properly due to the RFC standard that Zendesk uses, as noted here. The customer made updates to their Salesforce environment to resolve the problem and the issue now works just fine. 

We recently implemented Side Conversations and communicate via email with them. However, the replies to our side conversations are not threaded there but are creating brand new tickets (very annoying!) But the replies to tickets still thread without issue.

Is there a way to resolve this? We did not expect the threading logic to differ between tickets and side conversations.