When someone replies to your own Story or when someone mentions your Instagram account in their Story, these will be synced into your Agorapulse Inbox / Listening.
Story mentions and replies to Stories are part of Instagram Direct messages. To be able to see them in Agorapulse, you'll need to activate this feature first.
When someone mentions you in their Story, this will appear in the Listening section under Story mentions. As the conversation goes on, it'll move to the Inbox and will be under Direct messages.
When someone replies to your own story, this will appear in the Inbox section under Direct messages.