Well, the time-reversed waves can't have the same electric and magnetic fields as the original forward waves, because they travel in the opposite direction. In principle the reversal can be achieved by flipping the sign either the electric or magnetic fields. This reversed wave still would "look like" the reversal of the original wave, as the light intensities match.

In practice I expect that the mechanism to be much more involved than this. Traditional holography works by capturing a fine grained picture of light intensities on a surface or even in a volume, but it doesn't capture all possible information, certainly not both the electric and magnetic fields at a given time point. It looks like the researchers use a novel holographic technique to capture more information than normally possible.

> In traditional holography, a 2D diffractive element encodes the complex amplitude of a 2D wavefront, which can be recreated by illuminating the element with a spatial reference beam. This new device can be thought of as an extension of this to an extra dimension; a three-dimensional (3D) diffractive element, which when illuminated with a reference pulse in a reference spatial mode, will reconstruct a fully volumetric optical field (2 transverse space and 1 time/longitudinal space). It is a type of reprogrammable space-time hologram.

https://www.nature.com/articles/s41467-%20020-19601-3