Occasionally (when looking at something I'd rather they didn't know about), the thought that my partner might have installed something that monitors all network traffic and what websites are accessed crosses my mind... But I don't seriously worry about that, because I trust the people I live with, and they wouldn't do things like that.
Maybe your family are less respectful, or think messing with people is funny? But it also might be an expression of social anxiety. It's a pretty typical symptom of anxiety to worry that other people are thinking about us, talking about us, noticing tiny things (when most of the time people don't actually care that much). So worrying about spyware could be a modern version of that?
I wonder if there are some simple tech soloutions you could implement? Even if you simply get a cloud based log of every time your phone is unlocked, you'd be able to spot unauthorised access while you're sleeping. But the real answer is probably working on your sense of security and trust. Do you really have reasons not to trust these people? And if they did find out what you did on your phone, would it really matter? As some of the other commentators have said, if you're secure in yourself, then your online activity becoming public shouldn't worry you.