You stay on the frequency for the airspace you're in. Simple as that.
The tower controller will coordinate with the approach controller before sending aircraft into the TMA, and if relevant the approach controller will give traffic advisory/ensure separation depending on airspace classification.
I'd be pissed if you just left my frequency when you're in my airspace
Edit: Whatever you do on your standby radio, is up to you..... but I dare you not answering me if I call you. Oh, and I'm sitting next to the tower controller, so if you mistakenly answer me on his frequency..... I will know!