Sub Sidekick does not have a specific feature that stops texts from being generated at certain times, since those are automatically sent whenever jobs post to the substitute services' websites. However below is information that might help you from receiving the texts at undesirable times. 

If you have an iPhone or an Android phone, there are links below that show how to keep text messages from being delivered for times you'd rather not receive them. These settings on your phone will keep you from being disturbed at any time you do not want text messages. You will then receive any previously sent texts once your 'do not disturb' setting is off. For instructions, click the link below based on what phone type you have:

Also if you use Aesop, you can learn how to manage your 'call times' by visiting the Aesop Learning Center here.