astronomy - What time scale is used by the JPL HORIZONS system?

I'm confused by the ust of the term "UT" in the description of time scales used by the JPL HORIZONS system.

Their manual states that

UT is Universal Time This can mean one of two non-uniform time-scales based on the rotation of the Earth. For this program, prior to 1962, UT means UT1. After 1962, UT means UTC or "Coordinated Universal Time".

and the key attached to the tool's output says

Prior to 1962, times are UT1. Dates thereafter are UTC.

My understanding is that UTC has leap seconds, so that there should be an extra second at the end of a day on which a leap second was added, but the intervals reported by HORIZONS lacks these, and look more like UT1:

 2012-Jun-30 23:59:58.000 2456109.499976852 
 2012-Jun-30 23:59:58.667 2456109.499984568 
 2012-Jun-30 23:59:59.333 2456109.499992284 
 2012-Jul-01 00:00:00.000 2456109.500000000
 2012-Jul-01 00:00:00.667 2456109.500007716 
 2012-Jul-01 00:00:01.333 2456109.500015432 
 2012-Jul-01 00:00:02.000 2456109.500023148

Even more confusingly, the data reported do in fact behave as if the times are UTC. For example the reported azimuth of Pluto at Greenwich for the times above changes by 0.0028° for each of the intervals but the third, where it changes by 0.0069°, a factor of 2.5 times the change in each of the other intervals, which is exactly what would be expected ((1 + 2/3)/(2/3)) if there were an extra second between 2012-Jun-30 23:59:59.333 and 2012-Jul-01 00:00:00.000. This, despite the fact that the difference in JD over that interval is the same as each of the other intervals, meaning that one can't expect differences between JD that span any leap seconds to line up with changes in data!

If the times and data are UTC, how can the differences between JD be uniform? If they're UT1 how can the data "jump" at the leap second?

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Note also that the form for entering queries describes "Delta T" as CC-UT

which means that if "UT" can mean UTC, this means that after 1962, $\Delta T$ is a discontinuous function, but my understanding is that $\Delta T$ is that a continuous function, TT-UT, where UT is not UTC (see note 1 here).