You stay logged in to Basketball Connect in your own browser, as you are now. When you are looking at your team's draw or a match's scoresheet, you tap the helper. It reads the text on that page and opens Jumpball with it, where the importer sorts it into games or player points for you to check and save.
It sends only the text of the page you are looking at. It never sees or stores your Basketball Connect password, and nothing runs on our side. It also copies the text to your clipboard, so if the hand-over fails you can simply paste.
The Basketball Connect phone app itself cannot run the helper. Use the browser version of Basketball Connect, or take screenshots of the app and add them in the importer instead.