To me, it seems like the Kyururu girl somehow brought Tasuku into something like her 'imagination' in order for him to remember their time together back on Earth. The parts from panel 2 on page 13 to panel 2 on page 15 look like they are part of Tasuku's memories, and not a part of Kyururu's 'imagination.' Once he remembered her, she pulled them out of this 'imagination' place and back to reality. How they went from laying on the ground to being under a tree, I can't really explain. Maybe her power is some sort of hallucination, so people can be in her 'imagination' while also interacting with things in reality.
I don't know why that gate appeared at the end though, maybe just a deus ex machina.