Are you referencing your iCloud.com email? I'm going to assume you mean emails in general, correct me if I'm wrong.
Mail on iOS is just an email client. Mail Notifications sync with the email server via the Mail app, this isn't a function of iCloud. Keep in mind you can typically use any email address in Outlook for Windows, through a browser in Firefox for Linux and in a 3rd party apps for Android. Reading/deleting an email on any of those devices will make the notification in iOS go away and vice versa. The settings you're using in your email client and the functions the email server supports will determine the duration of the notification after it was read/deleted on another device.
Goto Settings > Password & Accounts > Fetch New Data.
Toggle Push on at the top. Goto each account and select push if available, Fetch if not. At the bottle of the select the duration to check for email using fetch, you can set it from 15 to 60 minutes.
Push is a function where the email server informs your devices of data changes. This is usually the quickest way sync email data since it tries to do it immediately.
Fetch is the process of your device logging into the email server and checking for email data based on a time interval. If fetch is set to 30 minutes there is potentially 30 minutes before the Mail app logs into your email server and removes/syncs notifications from another device that has already logged into your email server and read/deleted emails.
Hopefully this helped clear up some confusion.