No, "Exit Rule" will not help. There is often confusion about what this action does, but it does not stop or cancel any delays, repeats, waits, or schedules/subscriptions of any kind--it just skips all actions that come after it (for that particular execution of the actions).
From your screenshot, it appears you did not tick the "Stoppable?" box on the repeat action. That should fix your problem.
Actions run in the order you specify (though there is no guarantee that a device will have completed executing a particular command by the time the next action runs). Actions generally correspond to commands on devices, for which I know of no formal list of what corresponds to what, but it's generally easy to figure out: "Turn on switch" runs the on() command on the device, for example.
Some "actions" aren't really device actions at all but are specific to Rule Machine, like "Delay" or conditionals. For those, I highly recommend reading the docs.
You can if you want to, but user code on the hub is written in Groovy if that's why you're asking. 
Some people are picky in insisting that Rule Machine isn't really "code"--and it isn't, though the UI displays what you've configured in a sort of pseudo-code. But it does still require you to think a bit like a programmer: what order you want to do things in, how conditionals (Boolean algebra) work, and an examination of how your triggers (the only thing that make your actions run on their own) interact with these actions, among other things.
In most cases, I'd recommend using one of the built-in apps. The Notifications app would be a good choice here if you had a "real" TTS device, as it can handle all of this configuration with just a couple clicks (both the initial delay and the repeat--that last thing was recently-ish added as a lot of people were previously resorting to rules for this common task). Alas, using the "virtual sensor" workaround on Alexa, you're using devices this app doesn't support, so, a rule it is! (You could certainly do a custom app, but that would probably be even more work.)