Step one: the microphone
You press the key. Android grants the app access to the microphone and shows an indicator on screen for as long as it is open. So the state is observable at any moment, and not something you have to take on trust from a page like this one.
The microphone measures air pressure thousands of times a second and produces numbers. A recording, at this stage, is nothing more than that: a long list of measurements describing how a membrane moved.
Nothing has been decided yet, and nothing has been sent anywhere.
Step two: those numbers have to exist somewhere
Recognition cannot happen on sound that has not been captured, so for a few seconds the audio exists in memory while it is being processed.
This is the step people are usually asking about when they ask whether dictation "records" them. Technically yes, in the sense that measurements exist. In the sense people mean, whether a file is kept that somebody could listen to later, that depends entirely on what happens next.
Step three: the fork
Here the two designs separate, and everything that matters follows from which one you are using.
Server-side. The audio is packaged and transmitted over the network to a remote computer, which runs a model on it and sends text back. During that journey the audio exists on somebody else's hardware. What happens to it there is governed by that company's policies, and none of it is visible from your phone.
On-device. A model file already on your handset processes the measurements locally. Nothing is packaged, nothing is transmitted, and the audio never exists anywhere except in your phone's memory.
You can determine which one an app uses in under a minute: turn off mobile data and Wi-Fi and dictate. If words appear, it was the second.
Step four: sound becomes text
The model produces words. From this point the audio has served its purpose and the useful artefact is text.
That transition is the important one, because text is much smaller, much less identifying, and does not carry your voice, your tone, your accent or anything in the background of the room.
Whatever anyone does with the text afterwards, the recording of you saying it is a separate question with a separate answer.
Step five: the text goes into the field
The words land in whatever you were typing in, exactly as if you had typed them.
At that moment the keyboard's involvement ends completely. What happens next is governed by the app you put the text into: the messaging app, the notes app, the browser, the email client, and whatever they do with what you write.
This is the limit of what any keyboard can promise, ours included. A keyboard cannot make a messaging app private, and nobody should claim otherwise.
Where each design keeps the audio, in practice
"In memory" is doing a lot of work in step two. With on-device recognition the measurements exist inside the app's own process for as long as it takes to produce words, and then that memory is reused for something else, the way all memory is. There is no file written, so there is nothing to find, delete or accidentally back up.
With server-side recognition the same measurements are also copied into a network request, sent across whatever connection you are on, received by hardware you do not control, and processed there. Each of those is a normal engineering step and each is a place the audio exists that it did not before.
Neither description is an accusation. It is just that one path has four places your voice exists and the other has one.
What survives afterwards
Three separate questions hide behind that one, and they get confused with each other constantly.
Does the audio survive? With on-device recognition there is no file and nothing kept. LocalType keeps no archive of your recordings: the measurements are processed and the words are what remains.
Does the text survive? Yes, in the app you sent it to, exactly as typed text would. The point of writing something down is that it survives.
Does anything about you survive in the keyboard? Your settings and any words you added, which stay on the handset. Android's cloud backup is deliberately denied the app's data, so those do not leave the device or reappear on a new one.
What LocalType does at each step
The microphone opens when you press the key and closes when you stop; there is no wake word and nothing listening between dictations. The model is a file in storage no other app can reach, and it is the only thing that processes the audio. No network is involved at any point after the initial download, and internet access is requested for exactly one purpose, collecting the model you chose.
There is no account, so nothing associates any of it with a person. The product carries no advertising, and nothing inside it keeps a record of how you use it. In a password field the microphone key is not offered at all, so the one category of speech nobody should dictate cannot be dictated by accident.
The questions this does not answer
On-device recognition answers one question and leaves several untouched. It does not tell you what your phone's manufacturer does, what the app you are typing into does, or what happens to a message after it is sent. Those are three separate systems with three separate answers.
It also does not make you anonymous. The person you are writing to knows who you are, and no input method changes that.
What it does answer is narrow and checkable: whether your voice is transmitted to a third party in order to become text. On-device recognition answers no, and airplane mode lets you check that for yourself without believing a page.
"Is dictation private" is a question nobody can answer for you. "Is the audio transmitted, and does a recording survive" can be settled in about a minute, for any app on any phone, and those are the two facts the rest of it hangs on.
One minute, on whichever keyboard you already have
Airplane mode, dictate a sentence, see what happens. If words appear, the recognition ran on the handset. If nothing appears, or it waits and then gives up, the audio was going somewhere.
Then look at whether the app has internet permission at all, which is visible in Android's app settings and takes another thirty seconds. A keyboard with no network permission cannot transmit anything, whatever its description says.
Those two facts tell you more about what happens to your voice than any policy document, and they apply to the keyboard you already have as much as to any alternative. Most people have never checked, and the answer is frequently not what they assumed in either direction.