This guide only applies to Microsoft 365 hosted Customers.
Xink will only apply signature if Fully Server-Side setup is enabled. (not recommended if for client-side setup).
Out of the Office message are processed on Exchange Server side only (Microsoft design) and that is why ONLY Fully server-side setup is able to apply the signature.
The recommendation is still creating it manually via Outlook Client (PC) or Outlook on the web (Browser). In fact, most of 'out of the office' message are personalized by end users so it's not relevant to automate it.