Yes it's normal. The autofocus system needs to receive updates from the system as fast as it possibly can to perform at its best. When in 24p mode the system is only imaging 24 times per second, and therefore feeding the autofocus system 24 images. Whereas in 60i mode it sends 60 updates per second. Faster updates = faster response.
Most of the time, I keep my focus on manual because of the auto-focus lag in 24p. However, I do use the auto-focus sometimes under some circumstances. Actually, Panasonic calls it "focus assist" when used in 24p mode. It can come in handy sometimes, if you know how to use it to best advantage. Just experiment and see what you can do with it and when to turn it off.
