According to Wikipedia, the rough timeline is that there were several standards in use by military and civil aviation in the 1940s and earlier, including separate standards for Latin America and elsewhere, and these used Zebra in the US and UK. The International Air Transport Association presented a draft in1947 to the standards body International Civil Aviation Organization that was meant to rectify this, but it still contained Zebra. Apparently this alphabet wasn't good enough, because the ICAO hired a linguistics professor to create a revised alphabet, and it's this one that first contained Zulu, published in 1951.

There were several subsequent revisions following this, where the words were tested in university laboratories in the US and UK, before the final list was broadly adopted in 1956. Interestingly, according to this document written in 1959, the team that was revising the 1951 list attempted to replace Zulu with Zebra, but found that it didn't help the intelligibility of the alphabet, so Zulu was kept in the final standard.

As the next step in the modification, three more words were changed, FOOTBALL, UNIFORM, and ZEBRA were selected for insertion in the alphabet and a new series of tapes, training, and test sessions were instituted. As previously mentioned, the intelligibility of a word is seriously affected by the company it keeps, and it is therefore necessary to test a substitution in the context of the entire alphabet. Articulation scores for individual words should be used only as indicators of the word's performance in a given context.

A study of the comparative scores on the two modifications and the original ICAO alphabet showed that although the six-word modification [including three words + FOOTBALL, UNIFORM and ZEBRA] is superior to the original alphabet, it falls short in performance when compared with the first three-word modification [excluding FOOTBALL, UNIFORM, ZEBRA] -- more confusions were introduced than were removed by the second three-word modification, although these confusions cropped out in unexpected parts of the matrix. The problem is not unlike that of pushing a dent out of a child's celluloid ball -- even a successful push leaves a small dent in another place.