Pretty sure time goes wonky after achieving light speed not exactly sure on the specefics maybe the time dilation works as shown but I don't think the math is mathing here.
My simplest understanding of this (narratively) is that light took 10,000 years to reach her planet thus any image (gotta thank light for images) takes 10,000 years to arrive.
She can travel exactly 10,000 times the speed of light to planet Earth so when she arrives it's 10,000 years into the "future" (relative to the boy)
Who knew light speed was so slow
(What's funny is that the reincarnation of the boy was probably alive when she visited Earth the first time since it takes 10,000 years for an image to arrive to her so he's definietly dead now if he wasn't the first time great speed but unfortunante timing lol)