It depends on your league setup
I'm in three (all on ESPN) and one is based on FAAB, one is regular waivers which was set to teh revers of the draft order and that only changes based on waiver claims (as you described above), and in the other the waivers reset each Tuesday to the inverse order of the current standings (this week the lowest scoring 0-1 team would have the #1 priority).
If you're on ESPN look under the "settings" tab on your league homepage
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