While I like both of the existing answers (and it seems the OP is pleased), one of them appears to be an analysis-type answer and the other appears to be a behind the scenes answer. The question, however, is about plot explanation and asks about the connection between Gloria (the character) and Seoul - so I thought I'll just add an answer to the question as asked.
The in-universe explanation to the monsters' appearance in Seoul is simple: The model city Gloria made for her school project? That was Seoul.
So the scenario is this: Kid Gloria worked hard on her project and created a very detailed model of Seoul complete with many of its famous buildings and its cherry-blossom landscape. Oscar's project, on the other hand, is quite shoddy. It's a model of Madrid but he spelled the name wrong ('Marid') and it's basically just a cardboard box with a plastic toy cow in a bullring made out of popsicle sticks (and what looks like a very crude rendition of Plaza de Cibeles in the corner).
So when given the chance, a jealous Oscar stomps on this model of Seoul (just like his future self would do to the actual city), enraging Gloria. And one cosmic storm later, their emotions somehow manifested themselves at that very moment through their dolls... that now appeared in the real Seoul.