In the expansion, each Ruler will only begin appearing on missions after they have first been encountered during an assault on an Avatar Project facility.
The next ruler typically won't appear until the previous one is killed or successfully escaped. The first to appear is the Viper King, then the Berserker Queen and the last is the Archon King. The player cannot encounter multiple rulers in the same mission. The three Alien Rulers introduced in the DLC are: the Viper King, the Berserker Queen and the Archon King. Alien Rulers are new enemies added to XCOM 2 through the Alien Hunters DLC.