When Kun is imagining what it will be like to take his sister outdoors, notice that in a shot of Mirai in her basket show, the background is also in the outdoors. This is a blink-and-you'll-miss moment, but it's meant to establish that Kun has a very active imagination. As ambiguous as it is, it does explain why Kun experiences all these strange things in the story, from encountering his sister as a teenager to meeting Yukko as a human "prince".
Alternatively, notice how every time Kun experiences these strange happenings, the tree in the courtyard starts glowing. He met "Prince" Yukko while having a tantrum in the courtyard, met his grandfather while claiming he would quit bicycling in the same courtyard, ect, ect. The brilliant part comes when one realizes: that tree is Kun and Mirai's family tree! It's not just magical: it's the culmination of their family history responding to any problem Kun has in the present.
