Apparently, Carthage used primarily mercenary armies. How were these armies paid? Was the payment solely to support them with food and lodging, or was there another kind of payment that went to them, their home cities or tribes, or their families?
There seem to be two seperate questions here, the first being a more general one and then the specific question regarding Hannibal's army.
In regards to the first question, there seems to be evidence that mercenaries were paid in coin, first and foremost. Matthew Trundle argues that many of the autocrats, that came into existence in from around 700 BCE and forward, in Greece used coins to pay their mercenary armies.
Peisistratus used the money he minted from silver mines in Thrace to hire mercenaries to seize power at Athens in 546 BCE (Aristotle, Athenaiôn Politeia, 15.1–3).
It would also seem that there is a connection between the spread of coinage and the existence of mercenaries as a seperate group of soldiers.
There is little doubt that coinage facilitated the growth of mercenary service, for the great mercenary armies of the fourth century BCE could not have emerged without coins.
The distinction being that mercenaries were paid in coin for their services, as opposed to a citizen militia who were fighting as part of their collective 'citizen duty'.
I have found no mention of mercenaries per se being paid neither in land nor that there should be any special payments to their places of origin.
I do not seem to be able to find any definite sources on how exactly a mercenary's wage was spent, so whether they sent part of it home to their families or not remains unclear.
What does stand clear however is that the upswing in trade and the relative wealth of the Greek city states allowed for increasingly bigger mercenary armies. Therefore, it would stand to reason, since these city states were fairly small in terms of actual landholdings, that coinage was the predominant payment method for mercenary armies in the antique world.
(I hope this, at least to some degree, answers your question. However, this is my first post on askhistorians, so I'm hoping I did it right. I'm always happy to clarify.)
Sources:
Trundle, M. (2005), Ancient Greek Mercenaries (664–250 BCE). History Compass, 3:
Lewis, S. (2006). Ancient Tyranny. Edinburgh, GB: Edinburgh University Press. Chapter 1.