What I think is going on is that he took their paradox imprint using the machine. Then he went and did some ectobiology stuff (which is very much like alchemizing things).
In this case the 'captchalogue code' was the guardians' DNA. So first he just made normal clones because he just used their own DNAs. Then when he pressed the other button, he mixed the DNA of Grandma and Grandpa, and of Bro and Mom. Just like with the captchalogue cards they can be combined && (and) or || (or). This gives 2 different outcomes for each coupling. The Grandma+Grandpa clones are Jade and John and the Bro+Mom clones are Dave and Rose.
Somewhere later in the sburb session, when the meteors in the veil start going to skaia and it uses portals to throw these meteors to earth, 4 meteors with the baby Jade, John, Dave and Rose will each be launched to the past on earth.
On December 1st 1995, baby Jade's meteor hits the Betty Crocker factory owned by Grandpa Harley. The meteor crash is witnessed by Dad and Grandma (probably sparking Dad's interest in newspaper clippings about meteor crashes)
On December 3rd 1995, grandpa harley arrives with baby Jade on the pacific island and decides to settle there. Baby Jade is holding the bunny which was fixed by Rose. Becquerel is already on the island. In the city, baby Dave's meteor crashes into Bro's favorite record shop.
On December 4th 1995, Bro finds baby Dave in the smoking crater where his favorite record shop used to be. Then baby Rose's meteor crashes into the lake near Mom's laboratory, killing all the aquatic wildlife (like in the LOLAR). Mom adopts baby Rose.
On April 13th 1996, Mom is in the neighbourhood where the first meteor hit because Grandpa Harley told her to investigate them while he was on expedition. She brings baby Rose. Then she sees baby John's meteor heading for 'Prankster's Gambit', the family shop owned by Grandma and Dad. Dad comes outside to greet Mom, while Grandma stays inside, busying herself with Colonel Sassacre's book. Dad adopts baby John and probably becomes more interested in meteor crashes. Mom ran away and is seen on a cliff while baby Rose is holding the bunny before it was fixed, but it is already broken.
These dates are later seen as their 'birthdays', and they are apparently all adopted.
I think the paradox clones of Mom, Grandma, Grandpa and Bro are also transported back in time at some point in the Sburb session.
Yeah, I totally just typed that all out.
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