Is it obligatory to make up the day a traveler missed fasting in Turkey, given the differences in moon sightings and a 30-day fast in Egypt?

The basic principle is that a traveler should fast and break their fast with the people of the town they have arrived in. There is no harm upon you if you break your fast while traveling when Ramadan begins. You must make up for the day you missed fasting. This make-up is not waived by completing thirty days in your own country, unless you intended to make up for it on the "thirtieth day."