This is normal behavior, since database mail uses Service Broker, and queue, when you use sp_send_dbmail to send an e-mail, it gets put into a queue, which has an activation procedure on it. Service Broker ensures that the DB mail process will startup when needed.

You can see a log of what DB mail actually did in the MSDB database:

--messages not sent in past day

SELECT * FROM dbo.sysmail_allitems

WHERE sent_date > GETDATE() - 1

AND sent_status <> 'sent'

ORDER BY send_request_date DESC

--error log past day

SELECT i.mailitem_id, i.subject, i.send_request_date, l.log_date, i.body, i.file_attachments, l.description

FROM dbo.sysmail_faileditems as i

INNER JOIN dbo.sysmail_event_log AS l ON i.mailitem_id = l.mailitem_id

WHERE i.last_mod_date > GETDATE() - 1

ORDER BY i.send_request_date DESC, l.log_date DESC

see:

https://technet.microsoft.com/en-us/library/ms189635(v=sql.120).aspx