@James *****
Essentially, from what I've experienced first hand and from various accounts people have shared over the years, the consulates that accepted applications from foreigners not resident in the application country prior to the e-visa system, continue to do so under the current e-visa system for the most part.
Meanwhile, those which didn't accept applications from non-residents in the past are either continuing this policy under the e-visa system or may be more flexible now. China is one such country. One guy here said he applied from China using the e-visa system despite not being resident there.
Yet back in 2012, when I applied for a Thai visa in Kunming I had to prove I was a student, or on a working visa, which I was. Without one of those, they wouldn't have accepted my application. I only needed a tourist visa to cover my holidays (I didn't seek an in country extension as I only spent like 50 days in the country) then returned to China.