When uou two separate tickets with separate Passenger Name Record (PNR) and record locators, there is no obligation of the second ticket operators to make an accommodation for problems created by the first.

These are separate independent activities. Best to allow more than normal time for the connection between the separately booked itineraries.

That being said, most times the airlines will try to help you as a standby customer. Especially if the same flight operator is involved with both flights. So bottom of the list, but typically avoiding penalties.