Fly Postgres doesn’t support SSL, as far as I know. When you were connecting over .fly.dev, it was the Fly Proxy that was handling that side of things.
I.e., there isn’t a simple configuration tweak that you can make.
One possible workaround is to see whether the third-party tool will connect to localhost without SSL. If so, then you can put a repeater there that sends things over to the real database Machine.
Hope this helps a little!