Zoom Recordings

The answer is in the prerequisites section of this Zoom Support article:

https://support.zoom.us/hc/en-us/articles/201362473-Enabling-and-starting-local-recordings 

The bottom line is that local recording is not available except with the Zoom desktop client for Windows, macOS, or Linux, version 2.0 or higher. Phones and tablets can’t record locally. 

And note that recording to the Zoom Cloud is not available on Basic/Free accounts.