Hey Dea! Apologies for the confusion.
If you don't have the "All Sounds" turned on, what is supposed to happen is that the TextNow tab is backgrounded (it's not the tab you're currently on), and a message comes in, both the notification and the sound is meant to come on to let you know you have a new message. What seems to be happening right now is that it has the pop-up notification coming in, but the sound doesn't come on until you open up the tab again (so that is a bug that our engineers are looking into)
Otherwise, if you have the browser open to the messaging page and are actively on it, there will be no notification sound (as once again, it is only meant to occur when the tab is in the background)