This also explains why the other explorers didn't see Paradox Pokemon, because they didn't wish to see those creepy monsters.
Only after Sada/Turo used Pokeballs to catch them across time, the paradox Pokemon were able to start staying and inhabit in the modern time. (3/4)
So, if I want to explain how Terapagos's power works:
"Terapago/ Tera crystals have the power to temporarily summon humans or Pokemon from different times and space"
This is showcased by the professor's time machine, and we meet the professor in the crystal pool. (1/4)
One thing I want to point out, they don't summon random things. In fact, Terapagos doesn't decide what to summon. They only do the correlating time traveling upon reacting to wishes.
Heath/Sada/Turo wanted to see Paradox Pokemon, so Paradox Pokemon were summoned to them. (2/4)
This also explains the encounter with Sada/Turo in Crystal Pool.
Neither we nor Terapagos wanted to meet Sada/Turo. The wish of meeting them was from your giant lizard.
Look how happy they were when they showed up, and how sad they were when they left. (4/4)