Everything in MPF is driven by events, and those are handled in the order given. If you want to specify one event handler to be processed ahead of another, you can use the priority to guarantee (higher priority happens first) by adding a number to the event
event_player:
mode_base_started.100: start_first_mode
mode_base_started.60: start_second_mode
Note that each mode has its own startup routines that can take a number of cycles, so while the first mode will begin starting up before the second one, they will still be doing startup stuff at the same time. If you want to ensure that one mode is started before starting another, use the first mode's events to trigger the second.
event_player:
mode_base_started: start_first_mode
mode_first_mode_started: start_second_mode
Using specific events is the surest way to guarantee that one thing has happened before another starts.