Oh, wait a minute, I get it now. Ok -- so the clock doesn't move from 35 to 34 until a second has gone by.

Okay, when the clock strikes :59, it means there are 59.9 seconds left. Most new clocks have tenths on them once it gets under a minute, but not shot clocks. So, when the shot clock starts at 35, it will hit 34.9 (and leave off the .9) immediately. Therefore, when it first hits 25, there will be technically be 25.9 seconds left, so 10 seconds won't have elapsed until the clock gets to 25.0.
Ah, never mind. That's why I call it based on my count, anyway.

No. Because if that were true, then the buzzer would not sound immediately when the clock hits 0, since in your scenario it's at 0.9 seconds. To counter the 1 second delay, after the reset the clock will not move from 35 to 34 until a second has passed.

So when the clock displays 35, in reality the clock is at 35.0, 34.9, 34.8, ..., 34.1 seconds.

It changes to 34 at 34.0 seconds, which would allow it to display 0 at 0.0 seconds.