Yes, Ortigia island is a ZTL area. Only residents are free to drive in and out with no restrictions and park along the streets.
But the ZTL is not active 24h!
Timetables change depending on the time of the year and can be checked on the Siracusa municipality website.
Normally the floowing times apply:
DURING THE WEEK: active (no enter) from 7pm to 2 at night.
ON SATURDAY: active from 4pm to 7am on the following day.
ON SUNDAY AND PUBLIC HOLIDAYS: active from 11 am to 7 am on the floowing day.