I read that Roman soldiers were partially paid in salt, so wasting it on some sort of revenge idea seems very unlikely.
No. Scipio Aemilianus did not salt Carthage.
Ridley argues that there is no historical account or allusion to the salting of Carthage by the Romans [1].
Stevens [2] suggests that later sources indicated religious rituals were carried out at the site - one of these could have involved a plow in some sort of sulcus primigenius ritual, however, no salt is reported to been used in this way.
Stevens picks up Ridley’s argument and suggests that we must look to 19th century authors for the origin of the salting of Carthage [3].
Stevens and Ridley are both a good place to start for further reading on the subject.
[1] “To be taken with a pinch of salt: the destruction of Carthage.” CP 81 (1986): 140-146. R.T. Ridley.
[2 & 3] “A Legend of the Destruction of Carthage.” CP 83 (1988): 39-41. S. T. Stevens.