Black out on a rig or ship is very different to black start of a national electricity grid.
Most vessels will experience a blackout periodically and the emergency generator start fine, normally on electric or stored air start, and then the main generators will come up fine. It's really not delicate, complex or tricky - some vessels have black outs happen very often, and those that don't will test it periodically. There will also be a procedure to do it manually should automation fail.
There are air starters on some emergency generators that need handling pumping. These will also get tested periodically.
The most complex situation during black out restoration would be manual synchronisation of generators but this is nothing compared to a black start.
Most vessels will experience a blackout periodically and the emergency generator start fine, normally on electric or stored air start, and then the main generators will come up fine. It's really not delicate, complex or tricky - some vessels have black outs happen very often, and those that don't will test it periodically. There will also be a procedure to do it manually should automation fail.
There are air starters on some emergency generators that need handling pumping. These will also get tested periodically.
The most complex situation during black out restoration would be manual synchronisation of generators but this is nothing compared to a black start.