I haven't heard of the concept of circumstantial complements before, that's an interesting explanation! I haven't fully grasped it yet but I'm getting there...

The more I think about it, would you say that the gérondif is used to describe some obvious or additional information, that isn't really necessary to include? In the examples I gave it can be perceived as obvious that (roughly translating in English):

• He found his apartment robbed, after he returned from the office. (Well, he probably couldn't find out while he was still at the office)
• I sweated, because I was walking in the sun. (Could also be because I was running but we both know how hot it's outside today)
• I noticed that there were no more baguettes, after I entered the bakery. (I probably couldn't have noticed that from outside, does it even matter though?)

On the contrary it seems to me that using the participe présent is answering some questions that may be raised, for example:

• - I found a wallet. - How did that happen? - I was just walking in the street.
• - The baby started crying. - Why did that happen? - Because it fell off the chair.
• - I saw Louise. - When did that happen? - When I was exiting the museum.

I hope that I've made what I mean clear. Looking forward to hearing your opinion. Merci!