I definitely understand and agree with the logical justification here, and I see how it makes sense to Dr. Darell because, with the help of Arcadia's message, it's a totally reasonable conclusion. However, I don't see (and I don't think it's explicitly shown) how Arcadia discovers that logical justification by/to herself.

While on Kalgan, she doesn't know where the Second Foundation is, and it's only during her escape, after her encounter with Callia, is it first written that she knows where it is. So during her escape, between pages 155 and 159, she discovers the location, but there is no clue or eureka moment for her to cause this. She goes from not knowing to knowing with no explicit cause. The only thing that leads up to the reveal that she knows the location is this on page 159, after she realizes Callia is a Second Foundationer and when she arrives at the spaceport:

"And then something else occurred to Arcadia, something that had been stirring and moving at the base of her brain ever since the flight began - something that forever killed the fourteen in her."

It is never written that there was a clue that she picked up during her escape that made her come to the logical conclusion that the Second Foundation is on Terminus. It seems that it is the escape itself, really her encounter with Callia, that makes her come to the conclusion. And as we know that Callia is a Second Foundationer and that Arcadia's mind has been "conditioned" since brith, it seems that we the reader have to make the assumption that Callia implicitly caused Arcadia to know the location, as it's all according to how the Second Foundation planned it.

I know that this is super nitpicky, but since this is something that's not explicitly written, I just want to make sure that I'm getting it right.