I have no actual facts to contribute, but that’s never stopped me from posting before.
It would be pretty surprising if your computer’s interaction with your printer were routed over the internet for two reasons:
- Your phone is almost certainly using network address translation (NAT) as it bridges between your LTE connection (the internet) and the devices you’ve connected to your phone-as-hotspot. NAT is sometimes described as a firewall, which isn’t quite right—it prevents internet randos from connecting to computers on the other side of a NAT device, as do firewalls, but firewalls and NAT are different in other ways.
The point here is that NAT would prevent you from printing to that printer if your computer were trying to route the jobs over the internet and back in through the phone. This is the same reason internet randos can’t print to your printer à la the spam faxes of 20 years ago.
- You didn’t mention that you had to search for that printer after connecting it and your Mac to your phone. That implies that your computer is using the printer’s information from back when it and the computer were both on the same LAN. Printer discovery (“searching for the printer”) wouldn’t work across the internet (partly, but not exclusively, because of NAT). So if you’re printing without having to search for your printer, the data is almost certainly not being routed over the internet.
But! I bet the reason you’re asking has more to do with hotspot data use than the actual routing of print jobs. I would bet folding money that when you connect your Mac to your phone, all sorts of apps (and the OS) say to themselves, “Wow! A working internet connection! It has been so long! I must check for updates and silently download them while I can!”
So I suspect that silent update downloads consume a large amount of data when you connect your Mac. I recently moved and my iMac was in a box for a month. When I got home internet access and connected my Mac, it pulled down several gigabytes worth of updates. Even small apps (Logitech mouse drivers, I’m looking at you!) can suck up a hundred megabytes.
So yes, when you connect your printer and Mac to each other through your phone, you’re likely consuming a lot of data even though your print jobs are not part of that (those) data.
Do you have a wireless router or router/modem box from your old house? You can plug it in and connect both your printer and Mac to it. Neither will have internet access, but you’ll be able to print to your heart’s content without consuming mobile data.