If "the phone" sent out an SMS when it was off, it wasn't the phone doing it. (A phone with a dead battery can't send anything. The "messages" look like pocket dialing, or junk generated by someone else - the carrier's server going crazy or someone else getting connected as you because the SIM card number wasn't read correctly.
If it doesn't happen again, chalk it up to the crazy things that happen to everyone at times.
If it does, go into your carrier's repair store|department|whatever and ask them if they can figure out what's happening. (If it were my store, I'd give you another phone, transfer all your data to it, and let the manufacturer worry about it.)
08-17-2017 02:22 PM