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Since we're doing fun theories in this thread, this is about my thoughts on it. I don't necessarily think the professor set the coordinates in the time machine to the "right point in time", but I think they were able to harness the crystals which allowed them to access a world that doesn't exist within the boundaries of the normal spacetime. The anime mentions Rakua, a paradise that exists that no one can find. It may be a "lost world" type of scenario where it exists in its own pocket of time. "One second of your time is an eternity to me" type of scenario" trope which is how ancient/future pokemon exist.
I think with the next couple of encounters with Terapogos and Lucius' pokemon we'll have a better idea on how the whole "memory" ability it has and if you're able to interact with it or not. The OP implies Liko is chasing Lucius and eventually meets him, so I think in Indigo Disk we may either meet Heath or the Professor.
