What is the nature of the "unexpected geomagnetic pulse that took place beneath South America in 2016"?
The "geomagnetic pulse" here refers to a series of academic works studying the Earth's core such as this open access article (other related articles require scientific journal subscriptions to read).

Geomagnetic pulses have been associated with "geomagnetic jerks". A jerk was reported (yay for open access again) to have occurred in 2014, the 2016 pulse under South America is believed to be related to this, both events having been measured and identified after the fact.

The magnetic field is always changing - a "pulse" is a quicker-than-normal (few year) acceleration of magnetic field change in time, in a region at the surface of the Earth's outer core (magnetic field is generated within the core).

A "jerk" is a quick change (few months) of the rate at which magnetic field changes at Earth's surface, making something like a 'V' shape if you plot the field against time at a given location.

The idea is that a pulse occurs at the core, and jerks are an effect seen at the surface just before and after the peak of the pulse, as the field change ramps up and down. The underlying cause of this is not known, and we only identify them after they've occurred, so they're currently unpredictable. That said this behaviour is apparently part of the core's repertoire, and pulses and jerks have been observed before.