That's what's supposed to happen.
When you press and hold the microphone, it makes a chirp, and the light at the top of the remote turns blue
When you let go of the button, the remote makes a multitone chirp.
You will also get a blue light and a very different tone if the remote does not get a response from the set-top box that it (thinks that it) is paired to. (To test/experience this on a working setup, unplug power from the set-top box and press the Mic button on the remote.)
At the very least, when you press the Mic button on the remote, you should see some sort of on-screen response, even if you have Voice Control disabled in your Privacy settings. If voice commands are not working, you should also see an on-screen error message.
If you are not seeing any response, it's possible that you may have gotten your remotes mixed up. The easiest way to fix this is to reset the remote back to defaults (by entering setup code 981) and then redo the process of pairing and programming the remote.
You can also run into strange problems if the batteries in your remote are running low. To check this, go to Settings / Remote Settings.