The scholars of Fiqh have written regarding the sunnat of Fajr salah that if a person reaches the mosque without offering the sunnah of fajr salah from home at a time when jamah was already started, so if he can join the jamah after performing the sunnah, though in tashahhud, he should offer the sunnah of fajr in a placce near mosque like wudhu khana etc, and if such place is not available there, and the imam and muqtadis are inside the mosque, then he should offer in the courtyard of the mosque somewhere away from jamah. It is mentioned in several hadith that the companions of the holy Prophet Muhammad (صلى الله عليه وسلم) used to offer the sunnat of fajr salah after starting the iqamat of fajr jamah in their homes or near the mosque or inside the mosque near the gate. So, if it is hoped that one shall get imam in tashahhud after performing the sunnah, he should offer the sunnah in a place adjacent to mosque like wudhu khana etc if there is such place available; otherwise he can offer the sunnat in any corner of mosque away from the jamah and rows. The Hadith lay much emphasis on Fajr sunnat; hence the person who told you to offer the sunnah of fajr before the fardh is alright.
Allah (Subhana Wa Ta’ala) knows Best
Darul Uloom Deoband