Time travelling deductions
(last 2 paragraphs are my deductions about Chiaki's fate)
Chiaki was Makoto's age.
Makoto when leaping back, always leaped back to a time and place she was at. That meant there was only 1 timeline, and timespace continuum was maintained (roughly, she might land close by for example, but when leaping she'd always show up more or less in the same place she was at the time). When traveling back, she'd change clothes, and even her body to her earlier state (changing into pijamas, unburnt hair, and not having any injury) so she'd in fact be traveling back to her (a few days) younger body. So if Chiaki traveled back, he must have had already been born. That means the disaster is during Makoto/Chiaki's future lifetime.
He was from a different school, which is why there are rumors of him changing schools alot, and no one knowing where he is from, but since no one refers to him as a foreigner, he must have a japanese face and be japanese, otherwise kids would pick on that when referring to his habit of changing schools.
I also believe the knowledge goes with the time traveler. So even if Makoto traveled back and ate her pudding, when she returned she knew she had eaten it, but she didn't retroactively change her past knowledge (she didn't learn about time travel in the pudding day, although her conscience knew about time travel when she was eating it, the knowledge went with her back into the future) - this creates a time loop, because she'll always think her sister ate the pudding (which was true at first), ensuring she travels back in time and eats the pudding herself (hence not recalling it, and blamming her sister, perpetuating the cycle). That also means when Chiaki travels to the future, past Chiaki will probably not recall Makoto, nor anything else. Only future Chiaki will recall her. For him it'll be a split second and he'll look for future Makoto, but Makoto needs to live those days. Maybe it's just a couple of years. Maybe it's a couple of decades. Her aunt is caught in a similar fate, and the worst part is, that by becoming aware of the painting's relevance, they are proactively changing the future. That means her aunt restores the painting, and Makoto guards it. Butterfly effect is in full effect here, small changes nest big differences in the timeline in a matter of a couple of days. We manage to see her dying, as well as her friend dying. In a longer time, such a life devoting difference (devoting her life to protect the painting), will offer a radically different future (specially if the painting is indeed relevant and holds any power).
Maybe the disaster is even adverted due to the painting still existing in the future. It seems various time travelers have gone back to try and save the painting. The aunt is restoring the painting, despite it's apparent lack of worth and value in the present (she said so when she finishes restoring it) - the friend she is waiting for, probably told her of it, and it was from him she learned of time travel (she seems unphased by Makoto's experiences, subtly hinting that her subtle changes will bring big consequences and others might get hurt).
Maybe Chiaki's conscience/knowledge has nowhere to return to - the world he left is no longer there for the disaster was adverted, and so, when past Chiaki matures and gets there, he has no need to time travel and save the painting - avoiding meeting Makoto altogether, and never taking knowledge about her or even meeting her.
This is probably the case of the aunt's friend as well, and that's the reason she never saw him again.