It appears you have your incoming mail configured for the IMAP protocol on your devices, which will keep incoming mail on the email server such that it's available to all devices (i,e. received mail is "synchronized" across all devices through IMAP folders on the server). But this only applies to received mail.
The Exede/Wildblue email servers (like most) utilize the SMTP protocol for sending email, which does not provide direct support for saving a copy of sent email on the email server. Sent email is only saved locally on the device from which it is sent (when using a web mail client from your browser, this is on the server).
However, many email clients do provide the ability to save a copy of sent mail in an IMAP folder on the server. You'd need to dig into the settings for each of your email clients to determine how to do that if supported. Googling "save sent mail on IMAP server" may yield some insight.