I think @bigsnitch got confused because his mind is always working around Santorini
I believe @angeliki48 is right on the old and new port of MYKONOS (not Santorini).
It is true that there are ferries that also depart from the old port of Mykonos, still.
You really don’t have to worry about getting a print out of the ticket.
You can do it anytime from any travel agency on the island.
Most of the people get the ticket from the ferry kiosks or ferry offices that are just close or at the ports themselves.
You have to give them the Let’s Ferry reservation print out and you should be ok!
Honestly, nothing to worry about…
I wouldn’t spend the day before to do it but if you happen to pass by any travel agency while in Mykonos you can just pop in and ask them to do it for you! They are obliged by the law to do it…