Quick post to detail the steps to change permission mode for Project Server 2013 online. The default permission mode is the SharePoint permission mode, to change this to Classic permission mode (Project Server mode) see the steps below:
Open PWA and click Admin > Project:
Select the PWA site and click Project Web App > Settings from the ribbon:
Check the Classic permission management radio button, specify an administrator and click OK.
Please note, switching between permission modes deletes all security related settings.