Christopher,
If enabled, the "Confirmation" and, if enabled, "Welcome" messages are sent instantly upon subscription. Whether the message makes it to you is another story - your server could be experiencing temporary heavy mail load, slow delivery, etc, in which case your message could arrive several minutes or even hours later.
The first followup message, if configured with a delay of 0, would be sent the first time the scheduled "Dailymail" task runs, which can be 1 minute to 23:59 minutes after subscription.
Please let me know if I can be of further assistance!
Regards