Unix time is based on a hard calculation of UTC seconds, minutes, hours, days, and years. So UTC jumping causes a discontinuity in Unix time.
Im pretty sure the second graph is mislabeled (the UTC second after 23:59:60 should be 00:00:00), but Unix time takes 23:59:60 to mean the same as 00:00:00. So 23:59:60.5 is also the same as 00:00:00.5, and so on. If you parsed the Unix time into a readable timestamp, it would tell you it's the first second of the next day for two seconds.
Im pretty sure the second graph is mislabeled (the UTC second after 23:59:60 should be 00:00:00), but Unix time takes 23:59:60 to mean the same as 00:00:00. So 23:59:60.5 is also the same as 00:00:00.5, and so on. If you parsed the Unix time into a readable timestamp, it would tell you it's the first second of the next day for two seconds.