The activation of Office365 in Terminal Server environment is enabled with shared computer activation, but will not work without further configuration. What is not described in the Microsoft article, from my older blog entry, Office puts in the user directory “AppDataLocalMicrosoftOffice16.0Licensing” (the 16.0 stands for Office 2016, at 2013 there must be 15.0) a license token for the host (Server/Client). This token is valid only for the host on which the user has just activated the office. If the user logs on another host, a new token is placed in the directory.
For roaming profiles, the existing configuration must be extended by the folder listed above, or the folder that you defined with the GPO, so that it’s synchronized across all hosts.