In many retro-problems the stipulation asks who is to move in the given position, knowing that the default rule "White has the move" applies in positions where a retrograde analysis establishes that any side could very well have the move.
The question can be explicit like in the following example:
The Problemist, 1930
16+13. Who mates in 1?
Here it can proved that White played last, so that Black has the move (and gives mate).
In many problems the stipulation does not explicitly ask "who moves?". This is very frequent with a "Mate in 1" stipulation, which looks like a joke to the uninformed solver, but which often really means "who mates in 1?". As a rule, in all problems with a forward stipulation, the solver must check that the position is indeed legal, where legality includes side-to-move assumed by the stipulation.