When texting a user, who also has an email address associated with them, my "Notify requester of..." triggers still fire to send the user an email as well as a text.
By default, the user receives both a text message and an email notification with each new response from an agent. To only send texts, you need to modify your triggers to omit the Text channel.
To do this, add the condition Channel > Is not > Text, under meet all of the following conditions, in your triggers that notify your end users. If you use the proactive ticket functionality, as outlined in Proactive outbound texts, add the condition (Your Text Tag) > is not > present to your triggers to prevent it from firing when proactively texting.