Hi PriorKatieLIB-7720,
As I know, the alert icon is not related to other members in the same channel. You can get the alert icon even if other members view the information.
Make sure that when you post message in channels, it needs to mention the whole channel or someone.
For more information about channel notification, please refer to this article:
https://support.microsoft.com/en-gb/office/customize-channel-notifications-in-teams-c72b8c07-37e1-4a0b-82c9-fdfda04f15b2.
If I misunderstand your words, please provide us a screenshot to know your situation clearly.