Well, the thing is the whole interrogation was referring towards Rey's whole life. She was lonely and couldn't sleep so she thought of this island and ocean - not that she dream about them after she touched the lightsaber (there was not a moment she could sleep and think of that...cuz she was caught minutes after she touched the sword in first place...how can she dream about stuff when she even couldn't be recorded to sleep? )
Yes, there was a connection between her and Luke after that vision - revealed to her by the force - but that is still not explaining these memories/dreams she had before the whole adventure - when she was young. That is why I assume she got them by Luke instead the opposite.
As for their years, its really complicated to speculate when Kylo turned to the dark side (obviously he was not so young and from the vision Kylo was around 20+, with already build mask and saber with red crystal). Best bet is that by the time this purge happened, Rey was already at Jakku because Luke possibly had a vision of how things might turn or simply fears after sensing the confused mixed feelings of his nephew and simply prepared an early move.
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