Hello Dan:
That is exactly how IMAP and POP accounts work.
IMAP accounts will synch with the mail server and then update all your devices set up with that email account.
POP Works differently. When you use one device to retrieve/download email messages by using POP then the messages/emails are delivered to that device and are no longer on the server to be synchronized with other devices. See below for more information.
IMAP
IMAP allows you to access your email wherever you are, from any device. When you read an email message using IMAP, you aren't actually downloading or storing it on your computer; instead, you're reading it from the email service. As a result, you can check your email from different devices, anywhere in the world: your phone, a computer, a friend's computer.
IMAP only downloads a message when you click on it, and attachments aren't automatically downloaded. This way you're able to check your messages a lot more quickly than POP.
POP
POP works by contacting your email service and downloading all of your new messages from it. Once they are downloaded onto your PC or Mac, they are deleted from the email service. This means that after the email is downloaded, it can only be accessed using the same computer. If you try to access your email from a different device, the messages that have been previously downloaded won't be available to you.
Sent mail is stored locally on your PC or Mac, not on the email server.
A lot of Internet Service Providers (ISPs) give you email accounts that use POP.
Axel F.