'ad'+acc denotes movement toward something, but not into it.
'in'+acc denotes movement toward and into something.
'in'+abl denotes standing still or movement inside something, and is as such irrelevant here.
The most important thing to take note of, in this sentence, is that 'castra' in the answer key is in fact in the accusative case. 'castra' is one of the words that only appear in the plural, and is neuter plural of a hypothetical *castrum, -i - instead, you will find it in your dictionary under castra, -orum.
'ad castram', therefore, is incorrect.