Your phone does not have to be on anymore for you to see stuff your girlfriend looks at. Once they've made a statistical connection (and your phones keep regularly reporting from same IP for the foreseeable future) you will get the ads she looks at if they seem relevant to target to you as possible gifts/things-to-buy.
I sat through a corporate "ads data pipeline" info-session from Google for my company. You do not want to know the level of architecture pumping away in the background that collects and correlates disparate data about you together. It's actually shocking how robust and complex it is. Trust me, I've seen it, they know almost everything about you consumption/location/device wise.