I see your point. You are looking at the DDM right? Where, indeed, equity price increases as soon as dividends are expected to increase. However, remember that DDM is only correctly applied when dividends display (and will display) a very close pattern or relation to earnings result. If they diverge, DDM is not advised for equity valuation.
So, if dividends increase, E is also expected to increase, therefore P/E won’t necessarily increase. Also, this analysis (of DDM) has a long-term look of price and P/E.
The first case, in the other hand, is a one time event, where any dividend distribution decreases P and hence P/E. But, it is just a momentaneous effect.
I think I ran into this same issue when I was reviewing the chapter for Price and Enterprise Value Multiples. When practicing with a schweser Qbank, a similar question came up except that it was talking about the P/S ratio instead of P/E. I got the answer wrong because I was using the same logic as OP, and interestingly enough, this popped up in the answer explanation:
Note that the topic review does not allow for any interactive relationship between retention and growth. Thus, no explicit consideration is given to whether the increase in the payout ratio will cause an offsetting decrease in growth.
Not sure is this is like a CFAI issued statement, but it would be great to know so I don’t make a mistake like that on the exam. Basically, Schweser is saying “Don’t look that far into it”.