To my knowledge this is usually because the server responds to the browser's user-agent and serves content appropriate for the mobile device. If you override the user-agent and mimic a desktop browser, how would the traffic pattern be different then?

EDIT: I meant to state if you were to override the desktop's user-agent to mimic a mobile device while tethered.

An iOS device making periodic requests to https://*.update.microsoft.com might be one of many red flags.