It is a fact that the sun rises in countries located in South-East Asia before the Islamic countries in the Middle-East and Africa. Consequently, the day of 'Eid al-Adha starts here before yours (in Egypt), and we perform the 'Eid prayer, say the takbirs (i.e. saying Allahu akbar), and slaughter the sacrificial animals approximately four hours before you. If we slaughter on the day of 'Eid, after performing the 'Eid prayer, will this sacrifice be slaughtered before its proper time or not? Is it permissible for us to slaughter the sacrificial animals immediately after performing the 'Eid prayer, or should we wait until you perform 'Eid prayer (in Egypt)?

It is permissible to slaughter the sacrificial animals immediately after 'Eid prayer in your locality. This is similar to when you break fasts after the sun sets in your countries, not when it sets in Egypt or Saudi Arabia, or any other country and when you perform al-Fajr prayer when the day breaks in your countries, and do not wait for others, and so forth.
God Most High knows best.