Office 2010, IE 9 - IE10, SharePoint Online (SPO O365), when a user clicks on a document in a SharePoint document library two instances of the office application are started. Two windows showing the same document are opened by the single click in the document library.
**This workaround does have some side effects, lose benefits of the trusted zone settings**
In Internet Explorer go to "Internet Options" screen, and select the "Security" tab.
Remove the SharePoint online address from the trusted sites list.
This is a known issue and is actively being looked at by the product groups right now.
The estimated sever side fix date is sometime in March.
Even if it is removed from the trusted sites list, it still prompts to open twice.
You are correct, it does prompt to open twice, but only opens one copy if moved from the trusted sites.