You may be relived to know that Unix epoch time does not have this problem. But you may also be horrified to know why. First, epoch seconds are not the numbers of seconds since 1970/01/01. This is a lie we tell to children. Rather, epoch seconds are the number of days since 1970/01/01 * 86400 plus the number of seconds since midnight. Leap seconds, to epoch time, don't exist. Or maybe they are double counted. Or mayb…
Correction: We are mostly right, most of the time, but wrong in ways most people don't notice except if they try to talk while everyone is wrong.
Clarification: Human perception of time is not understandable, and the machine abstraction even less so.