According to rule No. 4 in this link, the suffix "-ist" does not affect the stress of a word. Hence the stress assignment rule
σ → [+stress] / ___ ((˘) σ) ]word should apply to both words. What makes them different from each other?
Taking economy into account as well, I think the problem doesn't come from the economist, but from economics:
economy has stress on the second syllable.
economist has stress on the second syllable too - hence, adding the suffix -ist doesn't change stress, like the site suggests.
economics has stress on the third (second-to-last) syllable and is thus different. I assume this comes from the suffix -ics; this suffix is not listed on the site, but -ic is and my guess would be that -ics behaves just the same, changing stress from the the second syllable to syllable before the suffix (i.e. -no-).
Therefore, the difference in stress between economy, economist and economics arises regularly due to the suffix -ics in economics, while -ist in econonomist preservers stress and is thereby equally stressed as economy.
This reasoning obviously presupposes economy as the underlying form from which we judge changes in stress. If we took e.g. economics as underlying, then things would indeed look different. But it seems just more reasonable to me to assume the semantically more "basic" economy as underlying and the other forms as derived.
Actually, to be precise, we should anyway start from the root (as econom-y has already undergone derivation and we can not just add a suffix, but most remove -y and then replace it by -ist or ics), and in the root econom- (if this is pronouncable at all - I assume you would find it nowhere free, I think this morpheme has the morphological status of a confix - a lexical morpheme which does not occur free but does not serve as an affix but clearly as a root, also e.g. fanat- in fanat-ic, so one can probably only judge the "standard" pronounciation intuitively and not from an underived form as such an underived form doesn't occur freely for such confix morphemes), stress should be on the second syllable as well - so neither econom-y nor econom-ist differ in stress from the root, like we would expect, while econom-ics does, like we would expect as well.
Under this assumption the stress behaviour fits well with the site's claims.