well im not sure how these clocks handle the leap second, or if they even display it. these "atomic" clocks that some people have in their homes arent really atomic, they simply receive a radio signal from NIST/USNO's atomic clock in Colorado, and thats how the "atomic" clock in your home stays synced.
So clocks' seconds display goes from 0-59 then back to 0 after incrementing the minute field, and Ive thought of 4 different ways they could be handled:
1) we actually see the rare 60 displayed in the seconds field
2) we see 59 for 2 seconds
3) 59 for one second followed by 00 for 2 seconds
now either of these 3 implies that that the clocks radios is always receiving, which would use lots of power and would quickly drain batteries of these types of clocks that use batteries. so this leads me to believe that #4 is what will prob happen.
4) the clock does as usual and just goes back to 0 after 1 second at being at 59. so the clock stays 1 second off until whenever the next time the clock's radio activates and checks the time.
so if either of 1 - 3 happens, we know your clock is always synced.
Look for 6:59:60 CDT tonight