I think of plugging in the definition as if it were a maths problem or something
Plugging in definition to
their economic circumstances are vastly different from those which pertained in their land of origin.
their economic circumstances are vastly different from those which (are or were) in effect or existence in their land of origin.
Hmmm...wait...actually I think either pertain or pertained works technically depending on the context, but I think the present tense pertain is kind of unusual an interpretation.
I think the intended interpretation is that 'they' migrated from their land of origin to wherever they are now. Thus, it's been awhile, probably years, since the migration and then during this time their economic circumstances are vastly different, probably vastly better. Hence, we use past tense.
But technically I can imagine the sentence with present tense 'pertain' in some kind of fictional story, say, fantasy where some genie grants 'their' wish to become richer and live somewhere else. Then I guess you'd say the present 'pertain' since it was only a few minutes ago since their economic circumstances changed.
Note: As for the exact cut-off between a few minutes and years, I think it's about if they've gotten settled already to their new economic circumstances. I guess even if years pass but they haven't settled somehow (maybe the genie takes them into the future?), you might still use present tense.