Wa `alaykum As-Salamu wa Rahmatullahi wa Barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
Dear brother in Islam, thanks a lot for your question, which reflects your care to have a clear view of the teachings of Islam. Allah commands Muslims to refer to people of knowledge to become well acquainted with the teachings of Islam in all aspects of life.
First of all, bear in mind that Allah has permitted the fasting person to eat and drink until dawn comes. He, Most High, says: (and eat and drink until the white thread becometh distinct to you from the black thread of the dawn) (Al-Baqarah 2:187).
The exact cut-off time for imsak (abstaining from food, drink, etc.) is the time of fajr (dawn); so if you ate until that time you did not incur any sin. Most of the time people confuse between the preferred time and the permissible one; the preferred time for imsak, according to scholars, is to finish sahur ten minutes before fajr.
In his response to your question, Sheikh Ahmad Kutty, a senior lecturer and Islamic scholar at the Islamic Institute of Toronto, Ontario, Canada, states the following:
You need not be overly confused about this issue, for it is merely a difference of opinion based on the distinction between what is preferred and what is merely permissible. There is no doubt that the cut-off point for consuming sahur is the arrival of dawn (i.e., fajr time). However, the preferred time for abstention is 10 or 15 minutes earlier than that.
The basis for establishing the preferred time of abstention (imsak ) is an authentic tradition from the Prophet (peace and blessings be upon him). One of his Companions narrated the story of taking sahur with the Prophet (peace and blessings be upon him). Upon hearing it, someone asked him, "What was the time gap between your sahur and fajr salah?" He replied, "The time required to read fifty verses of the Qur'an." It is estimated that this time can be 10 or 15 minutes and not more.
This, therefore, is the basis for the imsak time you are used to in Turkey. However, it must be pointed out that the above mentioned hadith does not state that it is not permissible to consume sahur later than that, for it only states that it was the sunnah of the Prophet (peace and blessings be upon him). As for the permissibility of consuming sahur until the arrival of dawn, it has been established by the clear text of the Qur'an: (Eat and drink until the white thread of dawn becomes distinct from the black thread of night) (Al-Baqarah 2:187).
Excerpted, with slight modifications, from: www.islam.ca.