Dfyjkt

My memory may be a bit foggy, and my Spanish comprehension was not excellent, but I will recall my experience as best I can. Maybe someone can shed some light on my confusion.

Begin from the United States, I am familiar with Daylight Saving Time, elsewhere known as Summer Time. I lived in Asunción, Paraguay, for a year in 2012-2013, where I managed the computers for a small non-profit organization. I arrived there in Southern Hemisphere winter. One day in the spring, I got to work and found that I was an hour late because the clocks had been set forward for "hora verano" (summer time). This was a surprise, but it made sense to me. I noticed that the computers had not observed the shift, even though their Windows time zone setting was "Paraguay." I reasoned that Microsoft had neglected to include Paraguayan summer time in its settings, and I manually set all the computer clocks forward.

A few weeks later, all the computer clocks shifted forward an hour. When I asked why, it was explained to me that while this was the official starting date for summer time, the government had declared that it would start a few weeks earlier than the official date. Also, they do this every year.

Maybe I misunderstood something, but if the government doesn't like the official start date for summer time, why don't they change it?

From Wikipedia:

Paraguay observes DST under decree 1867 of March 5, 2004. DST ends on
the second Sunday of March and starts on the first Sunday of October.

In 2007, DST started on October 15, 2006 and ended on March 11, 2007.

In 2010, Paraguay changed its own DST rules because of the energy
crisis, ending DST on the second Sunday in April, a month later than
previous years. The start date remains unchanged.

which is clearly somewhat deficient as it does not report (from timeanddate.com):

Published 7-Mar-2013

Paraguay ends Daylight Saving Time (DST) at midnight between Saturday,
March 23 and Sunday, March 24, 2013. The switch comes 3 weeks earlier
than planned. The South American country was originally scheduled to
switch back on Sunday, April 14.

Clocks in Paraguay will be turned back by 1 hour from midnight to
11:00 pm (23:00) local time.

With the reason given by the same source as:

School children's safety

The change of the DST schedule was announced today, March 7, 2013, by
the president of the National Electricity Administration (ANDE),
Carlos Heisele. According to a statement issued by ANDE, the date
change is designed to ensure the safety of school children who usually
have to make their way to school in the dark during the last weeks of
the DST period.

Paraguay usually begins observing DST on the first Sunday in October
and switches back to standard time on the second Sunday in April.

The same site keeps a very comprehensive list of updates but the 2013 entry for Paraguay seems to be its most recent at present.

The Decree mentioned in a Comment by the OP Decreto No 1864 of 2014 supersedes 1867 of 5 March 2004 (the one mentioned by Wikipedia), 3958 of 17 February 2010 (presumably in connection with the energy crisis) and 10780 of 15 March 2013 (presumably the one shown published 7-Mar-2013 by timeanddate.com). Wording includes (my translation):

Clocks go back one hour on the fourth Sunday in March each year and forward one hour 
on the first Sunday of October each year, throughout Paraguay. 

Somewhat strangely, no time for the time change is mentioned but a separate link provided by the OP suggests that the convention is to adjust once midnight is reached (for the first time) and that IATA say transitions occur at 00:00.

The Decree gives the reason as being to save electricity.