So you're telling me if we miss the flight from Athens to Santorini we have to buy another ticket to catch the next available flight even though we've already paid for it?? It's on the same airline
That may be true, but you have two separate distinct contracts with them.One for transport from Rome to Athens. The other for transport from Athens to Santorini. The way you booked it, one has nothing to do with the other. Should you miss the transfer in Athens they might take mercy on you and not make you buy another ticket, but they have no obligation to do so.
If you booked the Athens to Santorini as a r/t, i.e ATH-JTR-ATH, and you miss the ATH-JTR leg the return flight will be cancelled and you will need to buy a new return ticket.
Hopefully all works out, but this will be a lesson to not book flights as separate pieces, when a single booking can be done.
The positive thing is that the Aegean website shows it sells your 2 flights as a single booking, so there is a reasonably good chance you will make the transfer. If you have checked luggage, hopefully you will be able to check it through to JTR when you start in Rome. Having only carry on would be better