No, you really don't understand how Find my iPhone works. In order for Find my iPhone to know where you are it must use Location Services. If it didn't, when you went to locate your iPhone using another device with the app or by logging in to https://icloud.com/find it would have no idea where your phone was. So it periodically checks your location. That way it can also tell you where your phone WAS, 10 minutes ago, for example, even it is now out of range.
HOWEVER, if you shared your Apple ID you made a big mistake. You should NEVER give your Apple ID and password to anyone else for any reason. Even someone you know and trust. As you did you should change your Apple ID password, verify that your security questions have not been changed. And probably add 2 factor authentication to your account. And NEVER share any password with anyone again.
I have been in the computer field for 40 years. I've had passwords of various kinds almost since the beginning. And I have never told anyone any of my passwords. Even when my IT department needs access to my computer, I enter the password for them. And they understand and approve. After all, they don't want the responsibility if my account was ever compromised.