The verb tense has nothing to do with this. The question is whether the preposition during can be followed by a gerund (an -ing form acting as a noun).
Most prepositions can be followed by a gerund, but during is one of a few that only rarely can. Generally, if there is another noun that can be used instead of the gerund, the gerund cannot be used.
You could say during a/the/my/his, etc. walk, but not
When reading has a countable meaning — a public reading aloud from a book, such as during a religious ceremony or a promotion for a book — you could say during a/the reading. But you can't say something like Last night
during reading I heard the phone ring.
I suggest that you just teach your students that during cannot be followed by a gerund. That is what would be expected on an exam. If they need to use a gerund, they should use while.