When the ex-dividend date for a stock arrives, when during the day does the stock drop?

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I observed two stocks, and both of them seemed only to have priced in the ex-dividend date at around 9:30 AM, as opposed to other people saying that it happens at the beginning of pre-market hours. This has been a topic of great confusion to me, so I’d appreciate a more specific explanation.

In: 1

The price of the stock is only the last value it traded at. As the dividend is meant to be paid that day, in the perfect world it should drop almost immediately by the exact amount of the dividend.

However this doesn’t mean the stock can’t also still go up and down for reasons other than the dividend.

Let’s just call a perfect world. A $100 stock is paying a $5 dividend. As soon as the dividend is paid, that stock should be valued at $95.