By default, text message assignment reminders are sent out at 6:00am, however, you can change when the text messages are sent to you. Go to your Personal Profile then select the Text Messaging tab and change the times that text messages will be allowed. You can change the start time to a later time if you don't want to receive text messages at 6:00am. By default, text messages are allowed anytime of the day without restrictions.
For information about email reminder delivery times, you may refer to this support article.