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The Sage you have installed is running on your computer, and require no internet connection. When you use it using the Jupyter notebook, it launches a Jupyter server on your machine and connects your web browser to it. You will see that the url in the url bar is http://localhost:8888/tree where "localhost" indicates a connection to your computer, and not the internet.

You can run the Sage read-eval-print loop (or command-line interface) in the terminal (run sage in the terminal or change directory to where Sage is installed and run ./sage) or using the legacy SageNB notebook (run sage -n sagenb or ./sage -n sagenb), or using the Jupyter notebook (run sage -n jupyter or ./sage -n jupyter). All of them run locally on your computer.