The first jump in complexity was the appearance of the eukaryotes, a.k.a. nucleated cells, which also happened through hybridization through symbiosis of different kinds of cells.
The event discussed in TFA was the second jump in complexity.
After the ancestor of the red algae and green alga was created by the hybridization of an eukaryote with a cyanobacterium, eventually the cyanobacterium was reduced to a smaller cellular component named chloroplast, which is the site where solar light is captured, and a big part of its DNA has migrated into the nucleus, where it fused with the DNA of the eukaryote host.
Probably after a few hundred million years after the hybridization event, and after the descendants have split into red algae and green algae (the former are adapted to deeper water, which is not reached by the reddish part of the solar light, while the latter are adapted to shallow water with strong light, which enabled them to also spread on the continents, in freshwater), both red algae and green algae evolved multi-cellular forms, which was the next step in increasing complexity.
There is evidence of multi-cellular red algae and green algae from slightly more than a billion years ago. These are the most ancient living beings whose kind can be identified with certainty, because for most unicellular living beings identification is not possible without checking for features that are not preserved in fossils.
The multi-cellular animals, which brought another jump in complexity, appeared only a few hundred million years after the red algae and green algae, in a world where there was a surplus of food from the activity of the abundant algae.