As far as I can tell, there is a bug related to integrations and Unito. If you want to use the WrikeBot user (which is what Wrike recommend) then you can only select sync folders in your organisation which were created by the integration wizard. e.g. I can start an integration/sync and create a new folder, but I cannot use one that already exists. This means unless you plan things very carefully, you will end up with a messy folder structure.
You cannot share folders or projects with the WrikeBot user, add it to groups, etc... I think this would resolve the bug but support told me this wasn't possible.