EMPHASIS ON I DIDN'T DO THESE. THEY CAME FROM CHRIS MCFREELY'S SITE *WORSHIP* SO ALL CREDIT GOES TO HIS SITE AND TO JUSTIN WHO TRANSLATED THEM.
Tai's track is set in November 1999 (three months after the end of season one). He keeps hearing Kari's whistle, and, since it was left with Gatomon, he realises a gate to the DigiWorld must be open. He finds his Digivice, but it's not coming from it - it's coming from his father's computer. He communicates with Agumon, and the gate closes soon after - Kari is angry that he couldn't keep it open until she got back from shopping with their mother. This is when Tai first realises that communication between Earth and the DigiWorld is still possible.
(FF Agunimon made the following comments about this)
Joe's track is a phone conversation with his brother, Shin (His brother stuff gets horribly annoying he does have 2 brothers Shin was S2 + Jim S2...don't ask!), in May 2000, right after the kids released their Crest power. He mentions that Shuu is taking a class with Sora's father, and that Shuu was sleeping at a friend's house during the Greymon/Parrotmon battle at Highton View Terrace, while Shin slept through it. In a particularly nice bit of continuity, he reveals that he made the choice to become a doctor (you'll remember that he didn't want to in season one) because of all the pain and suffering he saw and was unable to do anything about in the DigiWorld.
Sora's track takes the form of a letter to her father in October 2000 - the two of them have been discussing Digimon and the DigiWorld since Sora met Biyomon again in May (when the Crest power was released). This explains why her dad was so well-informed in 02, when non-DD people were supposed to have forgotten about Digimon. Also, we learn that Sora started to play tennis because her mother was teaching her, as they've been getting along so well together. She mentions that she's hearing stories of her her mom and dad met, and that her class is going on a trip to Kyoto soon. (Makes sense since Yolei's class did)
Izzy's track, set in April 2001, sees him have an online chat with Gennai. The subject of the black ball Piedmon put in Gennai in season one's flashback in "The Ultimate Clash," is raised, but he explicitly states they don't know what it was for. The statement is also pretty much anon-sequiter, which supports the notion that it's just a little self-parodic nod and a wink from whoever wrote the track. (my theory of that is that it is to keep Gennai old) Izzy learns of Gennai's friends, and finds it odd that they "have the same face." It is not stated on whether it is old or young Gennai he is talking to, but young seems a good bet. He talks about Tentomon, mentions he's getting taller, but that someone in the year below him is still taller than him, and he says that he now knows the meaning of being a DigiDestined - it's not just having a Digimon partner, but is also being specifically selected to defend the DigiWorld. This helps us to know that in the future, where everyone has a Digimon, it does NOT mean that they are all DigiDestined. Izzy talks about how a new group of kids have been chosen, and that while the 01 crew want to help, they can't because these kids aren't from Japan - this can only be a reference to Michael and co. It's stated that these new kids aren't in Azulongmon's jurisdiction, and that Izzy and Gennai don't know anything about the other three Harmonious Ones.
Most important, however, is the big revelation in the 02 disc, which paves the way for the future where everyone has a Digimon partner - it sees Joe's brother (Shuu), Yolei's sisters, and June all become DigiDestined to battle a new evil in the DigiWorld.
XROS WARS (Young Hunters)