I've got a 5S IPhone. Details aside I was on some websites in private mode on safari browser, and somehow a certain someone found out. I made sure there was no history, cookies, nothing. Is it possible there's an app tracking my actions on my phone, and if so is there a way to hide it so that I wouldn't be able to see?
That's weird. I doubt there's actually software on your phone that's tracking you, but depending on how tech-savvy this certain someone is, there might be a couple ways they could see what you're looking at. They could also have gone to your ISP and asked to see what pages you visited, which is most likely what happened if you were browsing on a school or work connection.
Pretty tech savvy, but I was browsing on LTE and as far as I understand my phone company would only be able to see that, and he doesn't have access or information to the account.
It depends on your ISP but some will provide details like data usage information so that people can track where their data is going. Like if you have a 1GB monthly plan, for example, and you're constantly going over it, your ISP can show you "these websites are using up your data, see if they have mobile friendly versions or stop visiting them without wifi." Assuming you were watching videos, which uses a lot of data, that's probably what happened.
