I was soldering up a microswitch like this and I heard a pop once. Some internal spring gave way. I was using a butane portable iron for some reason rather than my temperature controlled desk unit.You're correct, of course, that they go to the inside. I'm basing my observation/guess on the typical switch design having the lugs held in place by the plastic case itself, so that if the lug is overheated much it'll deform the case...and my own experience from ages ago wiring up small switches and devices before I had a temp controlled iron.
Anyway, glad OP got this straightened out.