Insightly won't accept email messages that are auto-forwarded or auto-assigned via an automatic rule, so you'll need to forward emails to your Insightly mailbox individually. Insightly is not designed for this because invariably some emails you receive you may not wish to share with other users on your account, like social networking notifications, emails from friends, or spam messages.
Also, saved email counts against the storage maximum for your account. Excessive saved email may require you upgrade your Insightly subscription prematurely. If you use the Insightly Sidebar for Gmail or the Insightly app for Outlook 2013 you can save emails that are applicable to Insightly in just one click or forward them to your Insightly mailbox.