By default, responses in a BubbleIQ thread in Slack will post to Zendesk as a Public Response to that ticket, which will be visible to end users as well as agents.
You can still post messages as internal notes from Slack, by starting the message with IN:
Here is the result in Zendesk:
If you're looking to make all messages from threads post as internal notes, you can do that too. Here's how: https://support.bubbleiq.com/hc/en-us/articles/115003805614-How-to-make-messages-from-Slack-post-as-internal-notes