I'm Aware that Croatia operates some joint checkpoints with Slovenia and Bosnia, meaning both countries check you at the same location.
Are the crossings in Neum of this Kind?
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The crossings in Neum, or to be more specific, Klek border crossing and Zaton Doli border crossing, are normal joint border crossings. It means, that both countries have booths on each crossing, however they are not always occupied, so it may be that there will be only border guard from the country you are about to enter (meaning no exit control).
There may be additional person in the booth labelled "Carina", which is for customs official, in which you have to declare your goods, if they are taxable on entering.
Source: I have travelled more than a dozen times between Croatia, B&H and Croatia via Neum.