We have done this trip several times over the past few years with no crew issues at all. There are several ferries on the route and we just show up and buy tickets for whichever ferry is next.
The crews do tend to try and hustle people on board but I have not seen any rudeness. With regard to tickets, there are several booths at the port selling tickets for the various ferries on the route. I suppose someone could buy a ticket for one line and then try and board the ferry for a different line which would be an issue.
In theory, if you show up and go to a booth and request a ticket for the next ferry, they are obliged to direct you to the proper booth if it is not their ferry. We have never had an issue with that either and have, more than once, been directed to a different booth for the company with the next ferry.
One thing to be careful about is which ferry route you want to take. For our first few years going there, you could only get a ferry to Aegina Port. Last year, ferries started also running to Agia Marina on the east side of the island. While we stay in Agia Marina, there is not as much to do on a day trip as there is in Aegina Port and to get to the other side of the island you would need a car or to take a taxi. So we usually take the ferry to Aegina Port and rent a car for our stays on the island.