I've read the machaira family evolved from the khopesh-style "sickle swords" (or rather "sword-axes") of the Late Bronze Age and was pretty popular around the Middle East as well. If that theory is correct then it most likely arrived in Iberia through the Greek trading colonies, although imports through Phoenician merchants are another possibility (weren't quite a few of the Greek colonies around the western Med originally Phoenician ones anyway...?).

That aside, I've read the Iberian version usually called falcata differed from the East-Med original design mainly in having more in the way of serviceable thrusting tip, whereas the machaira/kopis type as well as their distant descendant the kukri are nigh exclusively "choppers".

The kukri most likely ended up in Nepal through Hellenic influences (ie. Bactria and its Indo-Hellenic successors) - recall that for example Hellenic influences on Buddhist religious art were considerable, and startlingly "Greek"-looking details survive on the older Buddhist buildings in Japan. Although as the machaira-type "chopper" was AFAIK also quite popular in Persia it may have travelled there equally well later or earlier too.