It will happen when Alibaba starts shipping to the Martian colony.
First, the assumption seems to be that it will be American centric projects that get to Mars first. I sincerely doubt this. It is going to take a sustained concentrated focused effort on the part of some efficiently centralized agency to accomplish the task, and currently the only country that fits the bill is China. They are the only economy that has the available disposable money under the control of a centralized command structure. The economy on Mars, therefore, would be a reflection of the economy of China, not of the West. It would be the Chinese economic, social, and cultural model that would be propagated and would prevail on Mars.
So to answer your question realistically, demands that we look at the type of economy China has, and to consider how that would transfer to Mars.
China has a history of some 8,000 years of continuous Confucian socialism, so it is unlikely that anything will change any time in the future. In China, the cultural focus has been on the benefit of society over the individual. The entire economic system, over thousands of years, has been centered on win-win non-adversarial negotiating. The first thing to realize, is that there are no 'sides' in this form of negotiation. (In China, the definition of 'fraud' is, basically, making money at the detriment of others). It is not zero-sum win-lose 'what I gain is taken from your loss' negotiating. All parties are striving for the most optimal solution for society, not the individual. Whatever is gained, is gained by and strengthens society as a whole. It is the philosophy of 'I can have this, only if everyone else can have something else'. In the end, 'profit' is a measure of how society itself profits from or gains from the transaction, the benefit of the transaction to society as a whole, not on some monetary gain or 'excess income over expenditure' of one side, or an individual.
Translated to Mars, this settlement would have as its main economic engine, the benefit and advancement of the colony as a whole, not of any particular individual or faction in it. Anything that was done, would be for the advancement of the society, of the entire colony.
So why is this important? In such a society, 'money' is no longer seen as an indication of 'wealth', nor of wealth accumulation. It would have no status within the society. It would probably be transient. That is, it would have an expiration date. If not used by such-and-such, it is null and void. It would be a mechanism of exchange only, a mechanism for immediate barter. It would also be a local economy only. Someone with a particular talent would produce something, that someone else would be attracted to. Perhaps a type of food, or an article of clothing, or an artistic creation. It's only value would be in its desirableness to someone else. So, a trade would be made, perhaps even with an intermediary exchange mechanism, a system of 'IOU's'. But what value would 'money' itself have in such an economy? Every person would work for the colony, not for themselves, as a collective. They would do what was necessary to keep the colony going, and would do jobs required of and for the colony, as part of their duty, not their employment. In return the colony would provide their necessities. Local goods would be made primarily for the use of the colony. There would not be sufficient demand for mass production, so things would be made on demand, as required, preordered. There would be no speculative manufacturing, as materials would be too scarce to allow for something to be made and then placed on a store shelf, waiting for demand. The economy would be immediate, not future speculative.
Such a colony would depend at first from supplies sent from earth. It would be very expensive to ship anything to Mars, and again nothing would be shipped speculatively. You don't send something all that distance 'just in case' someone might want it. There would be no 'Walmart' on Mars for a very long time. So that brings me to the first point - things would be shipped to Mars preordered and prepaid by the end user. It would be on-line shopping only. So this begs the question be asked, 'what would be the currency?' And the answer would be trivial - in the currency of the on-line shipper, using earth-based banks, bank accounts, and banking transaction methods. It would be conducted as part of the overall earth-based marketing of the retailer, part of their every day transactions. The volume of the Martian business in and of itself would not be sufficient to sustain a business enterprise. The Martian residents would need an earth-based bank account, and some mechanism for depositing earth-generated revenue into it, in earth-denominated funds. A Martian artist, for instance, who sold the artwork to earth-based entities. Or maybe even transient tourists from earth, who bought an all-expense-paid vacation from an earth-based business, using earth-based currency, paid to an earth-based corporation. But earth-based money would only have value on earth, not on Mars, and it would only have value based on what you could buy and ship from earth. The colony itself would be decidedly socialist and community-based in nature and design.