The sentence in the exam wasn't wrong
 

When something is still true at the time of reporting, we can keep the verb in the present or change it
to the past.
Grammar review Page 127
Therefore The sentence in the exam wasn't wrong and the answer (will be) is right

I think it must be " He just promised" or 'short time ago, he promised" or something like this
as we know present attracts present and past attracts past
what is your opinion?
thank you
مدرس غلبان
khairy fawzy

U r right , mr khiry