Homeostasis just likes possessing little girls I guess. Did the same to Maki in the flashback sequence in Tri.
More seriously though (although I legit kind of believe the above), as said before she's probably some kind of medium that is simply more attuned to these things than the others. Taichi needed to come back from the Digital World to see the Digimon in the news, whereas Hikari could see them normally. Perhaps this is because of the "children are more connected to Digimon" theme Adventure had, and Hikari was seen as the most innocent. Perhaps it's because Hikari did not repress the events of Hikarigaoka the way the other 7 did, and thus was more attuned to the Digital World going-ons (and the Digital World was more attuned to her). Perhaps it's because she spent more time with Koromon in the original OVA than Taichi did.
But it's more likely it's something she simply was born with. She did wake up before Taichi did, right as an strange digital phenomenom was happening around the area, and went to stand in front of a computer that was about to manifest a Digimon egg. No conclusive evidence of anything, but an interesting coincidence anyway.