This is still the case in the SourceTree 3.2.0 Windows beta that is only a few days old. When trying to authorize with https://dev.azure.com/OrgName, it seems to succeed in logging in, but fail at gaining Git permissions. Swapping to https://OrgName.VisualStudio.com works immediately. Remotes will work fine with the dev.azure.com format after this initial account authorization.

Any remote repository added using the old Generic Account / Generic Host method (3.1.3 on Windows still had no DevOps integration) should still work if you didn't regenerate the token those remotes use. If, like me, you regenerated your token you use for SourceTree so you could get the password, you will need to edit the DevOps remotes and select the new DevOps Host entry instead of the old Generic Host.