Its more or less random. I have run quite a lot of sites, and like
70% the Boss spawns solo.
20% the Boss spawns shortly after the last wave while you are still fighting it.
10% the Boss spawns right with the last wave.
I doubt that it has a special timing, because it even happens when shredding the sites with a 3000+ dps Kronos, you can’t kill the waves much faster than that.
If he spawns early, just focus him down while overheating your tank+weapons. If you can hold the normal waves without overheating, the added firepower from the boss should be completely be negated by turning on overheat for as long as you need to kill him. And always have a Hardshell5 and a Syth tank booster (either exile or blue pill) ready to take should you get in trouble because of an early boss spawn.