That's correct. You have to have 24 hours free from all company responsibilities, including any requirement to be on call. So, they have to put it on your schedule and you have to acknowledge it for it to count.

I assume you know this, but if you've had a 24 hour layover in the preceding six days, that resets the clock.

No requirement to check you schedule or answer your phone during the 24 hour break, however I would check your schedule just in case. I get a little fuzzy on exactly how early they can make you report after the 24 hour break.

*edit... I believe the answer is they can make you report 3 hours after the end of your 24 hour rest, if they put the trip on your line 9 hours prior to the end of your rest.