The sentence involves a compound subject joined by neither...nor, where the verb agrees with the closest subject. Here, the employees is the closest subject to the verb and is plural, requiring a plural verb (have submitted).
Option (C) has submitted is incorrect because has is singular. Options (A) and (B) are grammatically correct as parts of the compound subject.
Option (D) their reports yet is appropriate, as their agrees with the plural employees, and yet correctly modifies the timing. The corrected sentence is: Neither the manager nor the employees have submitted their reports yet. Note that the pronoun their in (D) is acceptable in standard English when referring to a mixed singular/plural compound subject for inclusivity.