Dear Daniel,
the green icon is done for this purpouse to download old messages history.
By default entering rooms or public chat will be downloaded messages exhanged in the latest 2 minutes.
If you want to increase this value, have a look at the following screenshot and change the highlighed setting based on your needs.
Setting 86400 seconds all the messages sent within the last day will be autodownloaded when entering rooms.
If your site exchanges a lot of messages having many users don't set a too high value, this could cause more bandwidth consumption.
Best regards,
John