Yes, the business is responsible for their poor decisions jus the same as the tardy employee is, one does not absolve the other.

The lack of overlap is its own problem but if you know there isn’t an overlap (from looking at the schedule) and you have even the most basic respect for your coworker then you will be at work at the time of shift change. Especially for shitty jobs people work in college you being 10 minutes late means you get paid less money so it’s not like the scummy employer is hurting the only person you hurt is your fellow proletariat coworker