@Retired2 -- when an email is sent to my Shaw address, does it first go to Shaw and then forwarded to my phone or does it go to both at the same time?
Shaw's mail-server receives and stores each incoming E-mail message. Compare this "delivery" to a Canada Post letter-carrier putting an envelope into the mailbox on the outside of your residence. Then, it becomes a "race" between your iPhone and your open WebMail browser-window, to be the first to "peek" into your mailbox on the Shaw mail-server. Compare to two residents each peeking, not at the same instant, into that mailbox on the outside of your residence. If one of the residents removes an envelope from the mailbox, then the other resident will not see the envelope. For your two E-mail programs (iPhone & WebMail), are you moving an unwanted message into the "Trash" folder on Shaw's mail-server, or are your "rules" choosing to "permanently delete" an unwanted message? If WebMail only moves the message, then the iPhone will still see the message.
I don't know which E-mail app you are using on your iPhone, and whether it can "filter" a message, based on words within its content, and then "permanently delete" the message. Maybe, see: https://support.apple.com/iphone to try to get more information about the capabilities of the E-mail app.
