https://www.bloomberg.com/news/articles/2018-04-02/stocks-lo...
These aren't two separate effects. The interaction between the buyback and the order-book is the mechanism through which the stock price is adjusted to take into account the smaller number of shares.
But there's also a second-order effect of the buyback on the share price. If the buyback is a wise thing to do (the shareholders can make better use of the cash than the business) then the shares should be more valuable after than before. I think it's this rise in the price that corresponds to the effect of buying the shares on the order book.
In the case of dividends, the price goes down. If the company distributes 10% of its market-cap as dividends, the price will go down 10% (actually less because a 10% dividend represents less that that to the recipients after taxes). And as time goes by the price will recover. If the net income (and therefore the EPS) remains constant, the stock price will get back to the original price when they accumulate again the cash they just distributed (at constant PE ratio).
Still, my point was that the long-term effect of the capital allocation choice (which cannot be anticipated by the market until they know that it has been made, or at least that it is going to be made, but in any case the information is not being incorporated into prices at the precise time of the actual transactions) is not the same as the short-term market effect. The capital allocation is usually implemented through a market operation but it doesn't even have to be the case (they could get the shares in an off-market operation, a real example is company A buying another company B which has a stake in A, they can then eliminate those shares). And even if it is done in the market, the effect on the price would be the same if any other party (let's say the Saudi Arabia sovereign fund) decides to buy a large position in the stock.
If the buyback is a wise thing to do, you say, the price of the stock should be higher and the price is adjusted through the open-market repurchasing of shares. The problem is that if the buyback is not a wise thing to do, the market effect of the buyback is still to push prices up!