This blog by a classicist claims that the word salary is indeed coming from the latin words salarium and sal, but that it is not clear what the connection is, that there is neither evidence for the explanation that Roman soldiers were paid in salt nor that it was an allowance for the specific purpose of buying salt:
http://kiwihellenist.blogspot.com/2017/01/salt-and-salary.ht...
Regarding the latter he writes:
"As I said above, ‘salt allowance’ isn’t a terrible guess. But I strongly suspect it’s much more metaphorical than that. Compare how the Greek word for a salary was opsōnion, literally ‘(money) for buying opson’, where opson means ‘fish, relish, sauce’. That doesn’t mean Greek workers were given a ‘fish allowance’: it means that there was a generalised idea that wages went on traded goods like fish, and not on things like barley which land-owners would grow for themselves. Similarly, in Rome, grain allowances were a common thing; it could easily make sense to interpret salarium as ‘everything-else-money’."
