I put in to get QB Arturo Tilghman off waivers. I thought the order was based on team records from the previous season. Last season my team went 0-16 while the Chargers went 6-10.

If it’s not based on team records from the previous season, then what determines the waiver order?

It uses the previous season's records up to a certain point, not sure exactly when. Then it goes based on this year's record, and idk what the tiebreaker is, since you both have 2-6 records.

I think it goes to reverse standings as early as pre-season. The tiebreakers would be the same as the regular standings (I think):
1. head-to-head game (if during this season)
2. division record (if in same division)
3. conference record (if in same conference)
4. record against common opponents (in NFL, but I don't know if MFN goes to this level).
5. net points scored (same as 4)
6. number of touchdowns scored (same)

The difference is that you want to lose these tiebreakers in order to get a higher waiver priority.
And I know that getting previous waiver claims impacts it somehow, but maybe only within the same mid-week period. Definitely impacted if you make more than one claim.