This was tested on Pebble Time HW 8.12 (snowy22), Pebble Time FW v3.2, Pebble Time app v3.1, iOS 8.4, and an iPhone 6.

The latest Pebble guide I could fine for setting up notifications on iOS (May 13, 2015) is not accurate, making it a trial and error exercise to customize notifications that get pushed to the watch.

Notifications are not dependent on the "Show on Lock Screen" setting or the "Alert Style" settings stated in the article. Alerts on the Pebble Time are actually tied to what appears in the Notification Center.

To disable notifications from a particular app, go to Settings → Notifications → <app> → Show in Notification Center → No Recent Items. When this is set to 1, 5, or 10, notifications will show up on your Pebble.

Security Note: If you’ve turned off the "Show Previews" option so text messages an email contents are not displayed on the Lock Screen, the message contents will still be displayed on the Pebble Time since it pulls content directly from the Notification Center.