(1) Connectivity change don't need to occur in regions that have activity change. The caudate could have a very constant response on average across all 4 trial types, but there could be modulation of the trial to trial variability that changes with trial type and hippocampal signal.

(2) An activated region is a region where the signal changes similarly across all trials of each trial type according to the HRF. A connected region is a region where the signal changes similarly across all trials of each trial type according to the neural activity in the seed region convolved with the HRF. As you can see, these are two fundamentally different signals. They can occur together or they can occur separately.

Hope this helps.

A word of caution. Do not use gPPI or PPI when the trial durations are set to 0. If you do, then you are testing the interaction of only the first 1/#time bins (default 1/16 or 1/8second). Anything that you are actually trying to capture in an interaction probably lasts more than 1/8 second. Thus you should model that duration of the interaction. The duration will have little effect on the shape of the HRF. The betas will change dramatically due to scaling of the HRF, but the statistics will be similar.