60D and focus issue in video mode

I am new to using video mode on my 60D. It is my understanding that when in Auto Focus (both the lens and the camera) it should automatically focus the lens without any input from me (other than initial focus). Here are 2 examples.

1) Face Recognition mode - When filming, I hold AF-ON and the white box focuses on my subject and then turns green. My subject is now in focus. I let go of the AF-ON button and when my subject moves further away or to the side the white box follows them but it doesn't keep them in focus. It should be keeping them in focus correct?

2) Live Focus - Anything in the white box should automatically be in focus right? Lets say I have 2 objects. Object A is 3 feet from me and object B is 10 feet from me. I place object A in the white box, hold down AF-ON until it is in focus and turns green and my subject is no in focus so I let go of AF-ON. When I move the camera so that the white box is now on object B it should automatically re-focus the camera so object B is in focus with no additional input form me right?

Since I have never done video before I want to make sure I am understanding this correctly. I tried with the 50mm 1.8, the kit 18-55mm lens, and a 100mm 2.8 macro lens. It will focus initially when I hold down AF-ON but then it wont track the focus along with the subject or focus box. Am I misunderstanding something? MAybe there is an additional setting I am unaware of?

Please help this video newbie! Thanks!

OK, I think from the research I have done that tracking is not possible in 60D. It looks like it started in 70D. Can anyone confirm? This would mean that while face detection is turned on, the detection only sets the AF point (the face) but you have to manually focus it yourself by holding down the AF-ON button. Am I correct?

I had the 60D & 70D. Neither had auto-tracking. That started with the 80D. I have that, too. It is a much better camera than either of its predecessors. Well worth the upgrade cost.