iPhone 5c does not alert imessages from email addresses
On the iPhone go to Settings --&gt; Notifications --&gt; Messages and make sure the following are all turned on, depending on what you want:


Allow Notifications
Show in Notification Center
Sounds --&gt; &lt;select sound&gt;
Badge App Icon
Show on Lock Screen


Under Alert Style When Unlocked select either Banners or Alerts, depending on how you want to be alerted.

As mentioned by @bmike, your Do Not Disturb setting will affect if the alerts go thru or not.