Dear Karny,
Let me explain with some arbitrary values. Depending on your threshold, let's say a voxel is significant if t value > 4. For your schizophrenia patients, maybe all voxels got t value < 4 and thus no 'activation'. Among the controls, maybe some voxels got t value > 4 and thus 'activated'.
In one tailed two sample t test [schizophrenia patients - controls], some voxels can be significant if the difference in t value is > 4, e.g. [3 - (-2)] = 5.
In this case, this voxel i has t value of 3 in the former group and t value of -2 in the latter group. The resultant becomes > 4.
Best,
Andy