Disabling online status does not grant complete stealth browsing. A widespread misconception assumes that switching off the green dot also shields you from alerting senders that you have read their notes.
The activity status indicator and message read receipts exist on completely independent logic tracks inside the application architecture. Your presence marker tells people you are holding your phone and running the app; read receipts confirm that your device fetched and displayed a specific payload in a chat.
If you turn off your activity switch but leave read receipts enabled, your followers will not see you online. However, the exact moment you open an incoming note, Instagram stamps the bottom of the conversation with a bold "Seen" label. That action instantly confirms your presence.
To achieve actual disconnection within direct messages, you must open your account settings, return to Messages and story replies, tap Show read receipts, and deactivate the toggle globally, or alter it on a chat-by-chat basis by tapping the recipient's name at the top of an individual conversation window.