How do we reconcile what was said—that affliction is for the disbeliever and tribulation is for the believer—with the hadith: "Calamity continues to befall the believer"?

The distinction mentioned in the question is incorrect. It has been established in the ahadith that both bala’ (affliction/calamity) and ibtila’ (testing/trial) are attributed to the believer. The ahadith have clarified that "the people most severely tested are the Prophets, then the righteous, then those who are most like them. A person will continue to be afflicted until he walks on the earth with no sin on him." And that "affliction will continue to befall a believing man or woman, in their person or their wealth, until they meet Allah with no sin on them." And that "the greater the affliction, the greater the reward. And indeed, when Allah loves a people, He tests them. So whoever is pleased [with the test], for him is pleasure [from Allah]; and whoever is displeased, for him is displeasure [from Allah]." The difference between bala’ and ibtila’ has been previously explained in a prior fatwa (definition).