Timing offset on direct fire engine

Why is common to adjust a 360º in direct fire (coil on) ignition?

I'm not sure if I understand your question correctly? If you're talking about the base timing or timing offset then with direct fire engines we can end up with the ignition timing at the correct point on the crank pulley when using a timing light but we may be on the wrong engine cycle and hence the spark occurs on the exhaust stroke. Adjusting the timing offset by 360 deg will correct this and put the spark on the proper engine cycle.