It's because "everyone" or "everybody" or whatever is a group that's treated as a singular noun. It's the same as "family".
It would be everyone runs to get their bags. If you say "everyone, run to get your bags", everyone would be a noun of direct address
....that escalated quickly. But she said everyone is a third person singular so what she basically told me is: Singular subject= Singular Verb Plural Subject= Plural Verb