Let's say that a worker gets paid weekly. On payday they cash their check and put some of the money into envelopes for their budget.

The act of paying the dividend is like putting the money into the envelopes to spend, that's not a process that adds value so we'd expect the price to offset the change. Over the next period of time though we normally expect the company to earn money and that's when we'd traditionally expect the price to rise. Just like the worker earns his pay until the next pay period.