What Was The Custodians Of The Chronology Reality?
The first new reality the timewave created was the Custodians of the Chronology, a macho, 1980's MacGyver parody timeline complete with cheesy opening credits. The Custodians were Dr. Nate Heywood aka "Steel", Dr. Ray Palmer aka "The Atom", Mick Rory aka "Heatwave", and Garima aka "Garima" (Garima is the three-breasted amazon warrior Mick magically dreamed up to fight Tagumo in "Tagumo Attacks!!!" and she remained on the Waverider as Mick's... girlfriend). The Custodians made their presence felt by murdering a leprechaun in 1962 Las Vegas.
The key changes are that the Custodians are swaggering, ultraviolent time bros who "shoot fugitives first and ask questions never". They keep a trophy room of the skulls of the fugitives they killed and they turned Mona's friend the Kaupe into a rug. The Custodians became this way because Sara Lance was killed by a unicorn in Woodstock 1969 during the season premiere "The Virgin Gary". Even Hank Heywood, who's now in charge of the Time Bureau after Ava went into mourning when Sara was killed, hates the Custodians (presumably because by killing the fugitives, they're ruining Nate's Project Hades scheme).
Constantine was imprisoned in the Time Bureau for "time crimes" and is going insane, but Charlie and ZariCat found him (Constantine briefly turned Zari human again and then quickly turned her back). With Ava and Mona's help, Charlie and John escaped the Time Bureau (as the Custodians and the Bureau's agents shot and killed each other), stole a Jump Ship, traveled back to Woodstock 1969, and blew up the unicorn before it could kill Sara. They thought that reset the timeline, but all it did was create a brand new one.
What Was The Sirens of Space-Time Reality?
The second new reality was the female Legends turning into the Sirens of Space-Time, a hair-flipping, karate-chopping Charlie's Angels spoof that again came complete with new opening credits. The S.O.S are Sara Lance aka "White Canary", Ava Sharpe aka "Roundhouse", and Gideon aka "Hard Drive", with Hank Heywood as their boss. The Sirens are every bit as violent as the Custodians were but... sexier.
Pretending to be Amaya, Charlie tried to join up with the S.O.S. but Gideon was equipped to sense shapeshifter pheromones and immediately sussed out that she's an imposter. Before she was able to escape, Charlie did learn that this time, reality was changed because the Fairy Godmother killed Nate, Rory, and Ray in 1692 Salem. After traveling back to Puritan times, Charlie shapeshifted into the Fairy Godmother and severed her magical connection to Prudence Hawthorne, the human girl she was bound to. This saved the Legends' lives so Charlie and Constantine assumed they had finally fixed the timeline. However, instead of ZariCat, Zari had turned into a puppet, which means the magical misfits actually created a third reality: DC's Puppets of Tomorrow.
What Was The Puppets of Tomorrow Reality?
Back aboard the Waverider, Constantine discovered Sara, Nate, and Ray had turned into puppet versions of themselves. This reality also came complete with new opening credits and a charming DC's Puppets of Tomorrow song where the Puppets sang about learning lessons and the importance of asking for help.
As for how the Legends transformed into felt versions of themselves, it turned out that thanks to Charlie and Constantine's meddling, the Fairy Godmother attached herself to Mick Rory instead of Prudence. Mick quickly reverted to his old life of crime and called the Legends "Time Bureau puppets", which the Fairy Godmother was only too happy to oblige him. So now, Mick and his new partner the Fairy Godmother are hardcore bank robbers.
Charlie and Constantine immediately returned to the Time Bureau and actually created even more alternate realities, but in each one, the Legends and the Time Bureau continued to die. Meanwhile, Constantine kept suffering after effects of breaking time that was tearing his mind apart. Finally, Zari talked the stubborn demonologist into doing the one thing he didn't want to do in order to set time back on course: he had to condemn Desmond back to Hell.