Can I add to this question a little? How did they recruit mercs who were light infantry, to be sent into a battle first essentially to be chewed up by the enemy while heavier troops and cavalry would flank and finish the job? How do you pay someone to essentially sign their own death warrant? Or is Rome II Total War lying to me by letting me recruit those types of infantry as mercenaries?
It should be stressed that the idea of Carthage relying on mercenaries is more than a little overdone and quite an oversimplification. Many of their troops were levvied from their own Libyan (and later Spanish) vassals; some would be allied forces provided under terms of prior agreement. But yes, some would be mercenaries, though even they were not all recruited the same way. Some men would hire themselves as individuals, but a great deal of the men hired from tribal peoples like the Iberians and Gauls would have come as part of existing units who followed a chieftain or leader. This man would offer his services to the Carthaginians, receive pay and then distribute it among his men himself. Important to note is that these men's loyalty was to their own leader rather than the paymaster who provided his money, and if said leader decided he was better off on the other side, his men would happily follow him- Goldsworthy mentions a Gallic chieftain who switched sides several times, betraying each of his masters in turn before moving on to a new one. Needless to say, it was probably not always the best idea to rely on these units playing a crucial part in your battle plan.
Oh, and /u/Implausibilibuddy has largely had his question answered, but as a rule: assume Rome 2 is wrong about everything and you'll do fine XD