Causative in Turkish, Hungarian and Japanese

I've found interesting coincidences among these three languages as far as the causative is concerned. First, the three of them add suffixes to verb to form the causative, which shouldn't be too surprising, since especially Turkish and Hungarian are called agglutinative languages (sometimes I think Japanese belongs to this category, sometimes I don't). And second: when the causative sentence has the doer and the doee, the doer is expressed in a different case than it would be if there were no doee present. Examples:

Hungarian: Leültettem a gyerekeket. Gyerekeket is in the accusative case.
Turkish: Çocukları oturttum. Çukları is in the accusative case.
Japanese: 子供たちを座らせた。(Kodomotachi o suwaraseta.) Kodomotachi is in the accusative case.
English: I had the children sit down.

But then you have:
Hungarian: Itattam a gyerekekkel vizet. Gyerekekkel is in the instrumental case.
Turkish: Çocuklara su içirdim. Çocuklara is in the dative case.
Japanese: 子供たちに水を飲ませた。(Kodomotachi ni mizu o nomaseta.) Kodomotachi ni is in the dative case.
English: I had the children drink water.

It makes sense objects should be marked in a different way when you have two in a sentence, but what puzzles me is why languages would favor two ways of organizing the causative rather than having the doer always in a specific case. I guess that what these languages need is the accusative case to be filled by something, whether it be the doer or the doee.