I just completed successfully a mission that included a 1hr XP point boost as a reward, and when I collected the reward did not receive it, nor do I believe I received the other rewards. I did get a message that rewards were collected, but unlike other successful missions, I did not get a list of those rewards.
You don't get an XP boost, it's just the same item. Hover the mouse over this item before starting or ending the mission to see a pop up which system gets boosted.
The boosts I discovered so far are skill boosts. (like +6 to photonic theory or +6 to starship attack vectors ... etc) They last for an hour. You can see the buff icon next to your captains (or ships) image in your HUD.