The remote control is made to have a connection from the browser to JOSM (send a command to JOSM to load a given object and/or area). Today this is done with https. For https it needs a certificate in JOSM. As far as I know, this certificate is not from the well known authorities the browsers know.

You can use the following URLs in Safari to ask JOSM for its version via https and accept the connection via https as an exception:
https://localhost:8112/version
https://127.0.0.1:8112/version

I don’t have a Mac here, but in theory this could be the reason, why it doesn’t work on your Apple computer.

Franz