The Mac app, Totals Export, reads the bank SMS stored in Messages on your Mac and shows you the transactions it finds. When you're ready, it sends them straight to Totals on your iPhone over your Wi-Fi.
Your iPhone parses them the same way it parses new messages and skips transactions it already has, so running an import twice doesn't double anything.
Nothing goes over the internet. The app reads Messages on your Mac, and the transfer runs directly between your Mac and iPhone over an encrypted connection that only the QR code opens.
Only messages from banks Totals supports are sent. Your other conversations stay where they are.
xattr -dr com.apple.quarantine /Applications/TotalsExport.app