It is fire-based. I was using Belias to try to fight the Bomb King one time (I was attempting to go for the Zodiac Spear after raithwall's tomb), and his Hellfire attack healed him. For those going for the Zodiac Spear early in the game and are using Belias to fight the Bomb King, that's why it's important to dismiss him as he's charging his Hellfire attack.
On the other hand, quickening concurrences are non-elemental and are considering physical damages. The Inferno concurrence, which looks just like Belias' Firaja when you fought him, did damage to the Bomb King.
That happened to me, too, during my first time through the Henne Mines. I thought I had to fight them before I could progress through. I didn't know I could oil and fire them. I just physically attacked them and used any random AoE spell (like Dark). Well, my guys kept getting confused, hurting each other, and they kept dying. It ended up resulting in a Game Over. ugrrh!!! I was so mad. I ended up turning the game off for the night. I then found out that I didn't have to fight them and that I could just run.
There's a similar mobbing incident that occurs in another gate junction in a secret area of those mines, but that one involves a different much much tougher type of enemies. However, for people who are wary and know of it, it's often referred to as the Ultimate Leveling-Up Room.
On the ship, some people trip the alarms on purpose so they can have more soldiers to fight in order to gain more EXP, LP, and items. They just keep coming after you if you do this as you said.
During a time while the alarms are on the whole time, some even stay for a while constantly fighting soldiers for LP. These people are usually a bit higher leveled, though (they generally had leveled a bit at the beginning). If I were to try chaining soldiers at this point, the sound of the alarms would get quite annoying.