Praise be to Allah, and may Allah’s peace and blessings be upon the Messenger of Allah, his family and his companions.

As to what follows:

In response to your question, we say, and with Allah Almighty lies all success:

What is most apparent is that if it is a live broadcast calling people to the prayer, then it is legislated to repeat after it because of the general scope of what is recorded in the hadith narrated by `Ata’ bin Yazid al-Laythi, from Abu Sa`id al-Khudri, “If you hear the adhan, then say whatever the caller to prayer says.” [Bukhari (611) and Muslim (383)]

However, if it is an adhan that is not calling people to the prayer – for example, if you are in Kuwait and you hear the call to prayer in Makkah – then there should be no problem in repeating after it, but it would not be included in the words of the Prophet (peace be upon him), “If you hear the adhan…” because this adhan is not calling the inhabitants of Kuwait to the prayer, as the time of prayer over there has already passed. 

This is what is most apparent to me, and Allah knows best.