And Hazel is distracted enough by the TMI that she doesn't notice until it's too late... And Cloud is just being a troll at the moment by not warning anyone or helping.

"Yuffie! No! Stop that right now!" She drops the Eevee she's holding in her haste to get out Yuffie's Poké ball because the bird is being unusually stubborn and ignoring her trainer while instead just trying to keep her balance. Just give Hazel a second, she has more than she's used to on her. A few are dropped on the ground as she digs in her bag for the right one.