The Reddit discussion references the Helms-Burton act, and for the case of things like banks and payment processors, I expect the problem is Title I section 103, which prohibits US nationals from extending loans or other financing to anyone for the purpose of financing transactions involving confiscated property as defined elsewhere in the act.
So for the cigar case, if the cigars were grown on land that was confiscated (for example), my reading of it is that processing a payment for the cigars would be prohibited under the act. Certainly so for MasterCard and Visa, which are clearly extending credit.
That's not the same as a blanket ban on both doing business with Cuba and business with US companies, but it does make things very complicated, I agree, especially because there are so many ways of extending credit when companies deal with each other.
The same happened with MasterCard and VISA, and is part of the reason why I think Germany should continue to keep its own payment system, and just ban MasterCard and VISA and PayPal within the EU.
Or that you can’t technically put apps on the iOS App Store or the Google Play Store if you trade with Cuba.
(As you technically need an export declaration, as described here: https://news.ycombinator.com/item?id=10835045 )