I repeatedly see problems like this and dislike them for one simple reason- they don't mean "rocket"! The whole point of a rocket is that they have an engine on board and can continue to accelerate, or at least not decelerate just with the acceleration due to gravity. But here, you are only given that the initial velocity so they must be talking about something thrown or fired upward.
Yes, Mitch is falling downward with, as you say, "Yo= 1000m V= 20m/s a= 0m/s^2" so that the formula Y= Yo + Vot + 1/2at^2 becomes Y= 1000- 20t. The "rocket" ("rock" might be better!) has Yo= 0m Vo= 125 m/s a=-9.8m/s^2 so Y= 125t- (9.8/2)t^2= 125t- 4.9t^2.
The rock will hit Mitch when he and the rock have the same height: 1000- 2t= 125t-4.9t^2. Solve that for t.