An interrupt event causes the increment to end on the current sub-pulse and automated turns to end. What the minimum increments checkbox does is to prevent automated turns from switching off until the specified number of increments have taken place. It doesn't prevent the interrupt event in the first place.
For example, assume you are launching missiles at an alien ship every 30 seconds. The game checks early in an increment to see if anyone is planning to fire anything and overrides the increment length if that is the case. As firing a weapon is an interrupt event, automated turns will end when you fire. This means you will have to press the time button after every missile launch. Using the min inc field, you could specify 20 increments and your ship will keep firing without stopping the game.
If an alien ship is launching missiles at you every thirty seconds, the game will do exactly the same calculation and make the max increment length 30 seconds. If you don't know about this alien ship, you will see the increments being shortened and not know why. However, as alien weapon fire is not an interrupt event (only damage caused to a player ship by that fire), automated turns would work normally and you wouldn't need to even use the min inc button. If you did have min inc switched on at this point though, the game wouldn't stop if that alien fire damaged your ship because you told it to ignore interrupts.
So to summarise, min increments simply prevents automated turns from switching off. It doesn't prevent those events that would cause automated turns to switch off. It doesn't prevent the game from ending the current increment before all sub-pulses have taken place and it doesn't prevent the game from deciding to change the length of the increment before it starts (because of weapon fire, or fleet interceptions, or an estimate that you are about to enter alien sensor range (or vice versa)).
Here is the original release note for that min inc feature.
"Sometimes, the interrupts can be a pain if they are stopping the game when you know you are just going to press the increment button again. This situation usually occurs in a battle when you are launching large numbers of missiles or its a close range energy engagement where you don't need to change targets very often. Therefore there is now a new text field above the Auto Turns checkbox called Min Inc (for 'minimum number of increments'). If you are using automated turns and enter a number in this checkbox, the game will run for that number of increments before stopping for any interrupt events. In other words, you are overriding all interrupts for a specified period. The Shift-F8 combo will still work to stop automated turns but, apart from that, no matter what happens the game will keep running increments until it reaches the minimum number of increments.
WARNING! Using this option will take away your ability to react instantly to potentially important events so use with great caution. This is an experiment to see how useful this functionality will be so I will appreciate feedback once v5.40 is out."
I have changed the popup text a little to make this clearer for v5.50 as the existing text could be interpreted to mean that interrupt events are prevented rather than ignored.
Steve
