Added would likely be used between multiple people.
"What happened to him?" I asked.
"He went into the house" Bart explained.
"He took a dump." Jim added.
Not the best and overloaded example but you get the jist. As I said before, the question is not when to use it, but if you are for or against their use.
And don't get me wrong, I don't think theres anything wrong about culling these words out. I just flicked through GRRM and almost all the tags are "said". So I know its fine that way too.
(Insert more badly done but hopefully illustrative spice and cooking metaphors here.)
That's the trick, though.
Speaker One is asking a question (and yes, if the speaker is actually asking a question and you need to tag it, always go with asked instead of said), so of course Speaker Two is explaining, he's answering a bloody question. Which makes 'answered', 'explained', and most of the rest of those non-standard tags purely redundant. Which is why most writers will use 'beats' (those little moments of action during dialogue heavy scenes), instead of tagging everyone all the time. And of course Speaker Three 'added' or 'clarified' or 'offered', again, that's obvious from the context. She's providing additional information, clarifying information. So again, purely redundant.
'What happened to him?' Zebra asked.
'He went into the house.' Bart nodded towards the shack.
Jim flashed a look of disgust then said, 'He took a dump.'
Not sterling prose, but look at the difference. In one you have a simple back and forth with redundant tags, in the other you avoid those redundant tags and add a bit to the characterisation and sense of place.
I know you're asking for a black and white answer, but as quite a few people have said, it doesn't work that way. The answer is: generally stick with said or asked, but when you think something else is vital to get the perfect nuance through to the reader, go for it. But again, intent and restraint. Like most things, once you're past learning the absolute basics of writing, there's not many 'always' or 'never' rules, except always do your best and never be boring.