He can give out his TextNow # as a completely separate #. The texts and calls show up in the TextNow app on the phone or on the browser app (https://www.textnow.com/messaging). Another person could log into his account on their phone but the messages would still show on the app.
He could just be texting from his TextNow # to his original # to see if it works. Doesn't mean he's cheating because he has a new TextNow #. Maybe he's just trying it out. TextNow is free and an awesome service. btw- The TextNow # isn't linked to your old # like Google Voice. It stands alone as its own service. You can have your original # texts and TextNow texts all show up in the TextNow app too.