Invoices are not immediately sent out via email unless you check the box on a client profile page and click the button to send it. There is an entire invoice delivery system that can send via email, paper, fax, and postal mail. The cron delivers invoices, and by default this occurs every 5 minutes when the cron runs.
See Settings > Company > Automation > Deliver Invoices.
If you are creating an invoice manually and want to send it right away, uncheck the deliver box, then manually send it after it's created by clicking the checkbox next to the invoice and submitting the form on the client's profile page.