If your invited users (collaborators) can't see your Instagram accounts, you haven't allowed them to have access yet. Only administrators can set users' account access privileges.
To set whether users can see particular accounts, visit the "Manage users" page under the menu in the left-side tool bar.
Then press the 'set access' button:
You can select which accounts the collaborator can see in the popup window. Users can see accounts that are checked (adventuresofquirky in the example below):
Then click "Set Access" and you are good to go.