Moto X (2014) Notification/Active Display issue

[phillygrl]

On my Moto X OG when I received a msg an icon would appear on the lock screen. I could touch and do a quick view or unlock, read and dismiss. On my Moto X 2014 (Lollipop) when I receive a msg, my screen turns on showing my wallpaper and shows a preview of the msg and who sent it. How do I stop this other than disable notifications with Active Display?