The CIA TOD only stores the time but not the date. Therefore the date set by clock_settime() ist just stored inside the C library for retrieval via clock_gettime().
The "very special" handling of 12AM/PM is based on https://groups.google.com/d/msg/comp.sys.cbm/ysVYSX4AMbc/vHrXCWEhCOUJ saying:
1. column ("24hr"): hour to be tested (decimal)
2. column ("Wr"): hour written to TOD register (BCD)
3. column ("Rd"): hour read from TOD register (BCD) immediately after writing the value in column 2 to see the conversion between AM/PM, if any
4. column ("Nx"): next hour (BCD) after the hour switch