Each minor faction that you do missions for can have an affiliation with one of the superpowers. The minor faction called the "Pilot's Federation Administration" does not have a superpower affiliation - they are Independent. You will not therefore see any superpower reputation bar when you do missions for them.
If, on the other hand, you are doing missions for minor factions aligned with the Federation (not the Pilot's Federation - they are two different entities), then you will see Federation reputation bars.
Gaining Reputation with the Federation does not do as much as it used to. It used to change the baseline friendliness for all aligned factions - so if you became Alied with the Federation, you became Allied with every single Federation-aligned faction in the game too. But now, all it does is give a modifier for the minor faction's reputation slider, so that missions give you more reputation points witht he minor faction.
Example: suppose it normally takes 20 missions of a certain type to go from Neutral to Allied with a minor faction. But if you are Allied with the federation and the minor faction giving you the missions is Federation-aligned, then you will only need to do 10 of thse missions to become Allied with the minor faction.
I also believe you need to be at least Friendly with the Superpower before they will start to give you ranking-up missions.
Finally, note that Superpower reputation does "decay" in certain circumstances. Specifically, if you go above 75% Friendly with a Superpower, then the rep will decay (at about 2% per day, I believe) until it drops down to 75% again. This effectively makes it impossible to become, and remain, at 100% Allied with all three Superpowers. Rep also anti-decays if you drop below 25% Hostile.