A mailbox's Message Template is used when replying to emails, however it is not used when sending new emails (i.e. pressing the Send Email button). If a template has been defined, it is generally something that needs to be included on all outgoing emails, regardless of whether they are new emails or replies.
Suggestion: in the Send Email page, use the template corresponding to the currently selected "From" address. If the "From" address is changed, change the template accordingly.