الجواب وباللہ التوفیق

Assalamualaikum Warahmatullah

1. First of all, such small Makatibs where children are not living (like they do in boarding schools) and there is no facility for their stay and food etc. or such schools where fees and tuition is being charged, generally they should not even accept the Zakat money. This is because such places are not considered as “Masraf” (i.e. places where Zakat can be spent) and due to the fact that sometimes Zakat money is utilized by such institutions in places where Zakat money should not be utilized.
2. If however such a Maktab or school has accepted Zakat, it is impermissible to pay the salary for teachers from it.

If there are such poor and needy students in these establishments who are eligible, can't even pay little fees and are deserving to receive Zakat, Zakat money can be given to them. If money cannot be given to them, then it is a must that the ownership of an object bought with Zakat money be given to them, without this process the Zakat will not be considered as paid. 

ولا يجوز دفعها إلى ولد الغني الصغير كذا في التبيين. ولو كان كبيرا فقيرا جاز. (الفتاوی الھندیۃ:۱؍۱۸۹، کتاب الزکاۃ)

فقط واللہ اعلم بالصواب