When I use photonic officer, it seems to only reduce the cooldowns of the currently activated powers (already in cooldown) If I click on a new power, the cooldown appears normal and the PO says it reduces the cooldowns for 60 seconds. Is this the way it is supposed to work? Or is it broken?

Last time I ran it it seemed to be working. You won't notice a jump on powers activated after PO is activated due to how PO is speeding your recharge. But if you use an ability that gives a 45 cooldown normally while PO is up, you should notice it now starting at 42-40 depending on your specs.

When I sit outside earth spacedock, I initiate sensor scan and the cool down is 1:30
When I initiate Photonic officer II, the cooldown drops almost 30 sec

If I initiate Photonic officer first, then initiate sensor scan, I still get a 1:30 cooldown.

Photonic Officer doesn't affect captain abilities, at all, afaik

Its effects should be the same whether the skill itself/another was first activated.