I kind of agree - you're right. The issue here hasn't actually popped up before. Usually when players are added to waivers it's on the day they debut. So waivers runs 3-4 days, past the 48-hour waiting period and there's no ambiguity. In this case, Spanky added Dodd to debut waivers before his appearance (like two days before). That would have been fine, but Spanky ideally would have extended the waiver period past 8PM tonight. He didn't do that, and Dodd came off waivers almost 24 hours before the 48-hour waiting period, confusing you.
I think the rule should actually be clarified with an addendum to the current phrasing:
Unowned players with no MLB experience that are added to a real life roster can only be added at 8PM ET two days after their MLB debut. So if they debut on Tuesday, they can be added at 8PM on Thursday. Commissioners reserve the right to manually add any such player to actual waivers, and owners can request that any such players are added to waivers. Waivers should expire at least 48 hours after their MLB debut. So if a player debuts on Tuesday waivers should not expire until at least Friday.