Admittably I made some shortcuts. Obviously chase does not likely have a relationship with that Turkish coffee shop, but it does have a relationship (which may be complex, involving visa, mastercard etc.) with the bank of that coffee shop.
So practically Chase says that now that you paid your coffee in turkey, we owe you a bit less, but at the same time we as a bank have agreed to owe that amount of dollars to the Turkish bank, who the on owes to the coffeeshop owner some turkish lira. (and someone makes also the currency conversion there). The banks have between themselves some credit/limit arrangement that they do not need to actually start moving "real" central bank money [1] every time I buy a coffee. At the end of the day, most of the time the customer payments should not have a systematic drift (if there were, it would be called bank run), so banks just work within these credit limits.
It may sound like turtles all the way down, but that is exactly what the modern financial system is. Credit all the way down. There is very little else than credit in the system.
[1 ]which the turkish bank does not even have access but that is one more complexity layer I ignore here...
