As for the time of Iftar,
Narrated Umar bin Al-Khattab:
Allah's Apostle said, "When night falls from this side and the day vanishes from this side and the sun sets, then the fasting person should break his fast." Sahih Al-Bukhari Volume 3, Book 31, Hadith 175.
Narrated Ibn Abi Aufa:
We were in the company of Allah's Apostle on a journey. He said to a man, "Get down and mix Sawiq (powdered barley) with water for me." The man said, "The sun (has not set yet), O Allah's Apostle." The Prophet again said to him, "Get down and mix Sawiq with water for me." The man again said, "O Allah's Apostle! The sun!" The Prophet said to him (for the third time) "Get down and mix Sawiq with water for me." The man dismounted and mixed Sawiq with water for him. The Prophet drank it and then beckoned with his hand (towards the East) and said, "When you see the night falling from this side, then a fasting person should break his fast." Sahih Al-Bukhari Volume 3, Book 31, Hadith 162.
The first hadith says we must break fast during sunset. The second Hadith asks us not to delay the Iftar till the sun fully sets. In short, it is logical to break the fast just at the beginning of sunset.
As for the timing of Maghrib prayer,
Narrated Jabir bin 'Abdullah:
The Prophet used to pray the Zuhr at mid-day, and the 'Asr at a time when the sun was still bright, the Maghrib after sunset (at its stated time) and the Isha at a variable time. Whenever he saw the people assembled (for Isha' prayer) he would pray earlier and if the people delayed, he would delay the prayer. And they or the Prophet used to offer the Fajr Prayers when it is still dark. Sahih Al-Bukhari Volume 1, Book 10, Hadith 535.
We used to pray the Maghrib prayer with the Prophet when the sun disappeared from the horizon. Sahih Al-Bukhari Volume 1, Book 10, Hadith 536.
Narrated Rafi' bin Khadij:
We used to offer the Maghrib prayer with the Prophet and after finishing the prayer one of us may go away and could still see as Par as the spots where one's arrow might reach when shot by a bow. Sahih Al-Bukhari Volume 1, Book 10, Hadith 534.
So, the Maghrib prayer is after sunset. Take a look at another Hadith:
Narrated Ibn 'Umar:
Allah's Apostle said, "None of you should try to pray at sunrise or sunset."
Sahih Al-Bukhari Volume 1, Book 10, Hadith 559.
Narrated Hisham's father:
Ibn 'Umar said, "Allah's Apostle said, 'Do not pray at the time of sunrise and at the time of sunset.' " Ibn 'Umar said, "Allah's Apostle said, 'If the edge of the sun appears (above the horizon) delay the prayer till it becomes high, and if the edge of the sun disappears, delay the prayer till it sets (disappears completely).' " Sahih Al-Bukhari Volume 1, Book 10, Hadith 557.
As for the delay in between,
Referring to all the Ahadith above, we may infer that the Iftar timing is just at the (beginning of) sunset and the Maghrib prayer timing is after sunset. Going scientifically, the sunset takes around 3-5 minutes depending on where you live. These 3-5 minutes + a few minutes after sunset (So that there is no ambiguity of timing) decided by the Mosque authorities + some time for the people to gather, come to a gross 7-8 minutes.
So, this delay is in accordance with the Ahadith.
ۚ وَاللَّهُ عَلِيمٌ حَكِيمٌ (And Allah is the All-Knower, the Wise)