In a manga that's so focused on plot and grounding the plot somewhat in reality, having perez show off clearing the rocks by being an Aura user feels really goofy. It's very difficult to help save people from a landslide. I feel like it would be just as much of an opportunity to show off the ML's good points by showing him as being knowledgeable about landslide rescue and managing a team rather than pulling out an Aura sword and fantastically cleaving rocks which could frankly cause a second landslide....it just feels so silly. And to ignore the casualties as well, as others pointed out.
I mean, Perez is desperate. And from everything we can see, everyone else is already doing as much as they can to help with the landslide.
He probably is aware of how to properly go about removing the rocks (if he really is knowledgeable on landslide rescue) so him doing the work of breaking up the bigger rocks while the equipment to do so arrives is the best he can do with his special abilities...while not having enough patience to try and coordinate a team of people, at least.
And Tia going to the construction site...I mean, yeah pretty dumb even without needing to predict when the landslide would happen: it was bound to, so being careful about when to move would be the proper thing to do. I'll just chalk it up to her being careless because everything had been going so well she let her guard down (besides the author wanting a dramatic situation).