You're right on both things. It's just that the BBs are contradictory. They follow the common sense logic, not the strict logic.
Yes, the first economic update was 23rd. However, in this case they consider the next Monday to be the first of this season. Why? Well, it's the first economic update, with the new salaries.
Yes, veterans wage drop isn't included into training exemption. It states that players salaries are taken upon their joining. It would mean that salary drops are included. However, since it's a training exemption, naturally, only the positive players are included.
Basically, if the site was run by a mathematician, or anyone who read Euclid's Geometry, there wouldn't be any logical contradictions. Unfortunately, it isn't the case :)