>>12358>I don't want them to see my traffic, or associate that traffic with me.
If using Tor they won't see where your requests are going or their content. But they will see that they're coming from you and can therefore perform a traffic analysis (size, timing).
Hypothetically speaking if they control a large number of Tor exit nodes (really doubt it) they could connect you to the requests you're making. If your requests go over TLS (e.g. HTTPS) after exiting the Tor network then they would learn only about the domains/servers you're visiting, but not the rest of the requests (URL, headers, payload) or responses.
I would worry more about the fact that you're using Tor at all - it could raise some alarms. You can mask that by using a Tor bridge. It's easy to configure in Tor browser, just look at the network settings. You can also request a publicly unknown bridge from Tor project via email.
This would still make your traffic unusual, but unless their detection system is really aggressive it shouldn't flag you.