Learn Turkish: Bu kötü haber yoksul insanları çok korkuturdu. - This bad news would frighten the poor people a lot.

By using the causative suffix. The root is kork- (fear). Adding the causative suffix -ut creates korkutmak, which literally means 'to cause to fear' or 'to frighten'.

What gives korkuturdu the meaning of 'would frighten' rather than just 'frightened'?

That comes from combining the aorist tense (-ur) with the past tense suffix (-du). This double-tense combination (-urdu) is used for habits in the past ('used to frighten') or the main clause of a conditional situation ('would frighten').

Why does insanları have the accusative -ı ending?

Because 'the poor people' are the definite direct object of the sentence. They are the specific people receiving the action of the verb korkutmak (to frighten), so they need the accusative case.

When using korkmak (to fear), we usually use the ablative case (-dan). Why isn't it used here?

You are right that the base verb korkmak takes the ablative case for the thing you are afraid of. However, adding a causative suffix changes the grammar of the sentence. The new verb korkutmak (to frighten) takes the accusative case for the person being frightened, because they are now the direct object receiving the action.