Repurposing is the way to go. No matter who made the base... whoever conquered it last and occupied it. That's Ilum.
Belsavis? Only the Republic had facilities there. The Star Cabal knew about it and simply inserted their own. There is nothing during the planet quests -- or the class quests to indicate otherwise.
Planet Quests;
Empire -- Are freeing the Dread Masters. Of which have been moved deep, deep into the lower depths. The bases are less-occupied the further you go, to the point that the deepest base isn't even manned -- it's automated.
Republic -- Are ending the threat of the Cow People. You've got people down there, but initially they've been pushed back and it's stated that the Rakatan droid Custodians are the ones that usually take things from there.
Class quests;
Jedi Knight; Most thrown-in story EVER. Crazy purebloods out to sacrafice a planet and they pick the one that happens to fight back the most? Right! They're out to take whatever facilities are out and blowing stuff up. You're fighting the empire the whole way -- none of which are actually their facilities.
Jedi Consular; recruit a faction of Cow People. You don't run into many Imperials (actually that's incorrect, I should just say they're there to impede you)
Smuggler; Recruiting Rogun's former boss. For whatever reason.
Trooper; Are recovering a war asset -- elite fighter pilots who're helping quell the riots. That just escalated.
Warrior; You're here to end the Bacan Baron's sister. Again, you're going through Republic facilities. Indicative of the Imperial presence being very recent and very new.
Inquisitor; You're here to remake... well, you. The facilities as you go down are Rakatan and that part of lore gets brought
Agent; Star Cabal. Enough said. You're working with a neutral group to get there... and it's definitely not Imperial whatsoever.
Bounty Hunter; you're here... to off someone. Someone who helped with Hylo Visz' breaking of the Mandalorian Blockade. Do you run into any Imperial facilities? No... the Belsavis facilities largely predate the Republican ones as indidicated by the NPCs.
[conjecture]
It is very possible that the Empire... or more accurately, certain members of the Empire knew about Belsavis but had no real reason to hit there before open conflict. Belsavis should have close to 0 Imperial presence during the Cold War.
Ilum can be justified. The Adegan crystals might have been discovered beforehand but it can be justified that the Republic really only cared when they arrived in force to claim the crystals. Again, default is... Republic presence. Could be that the Empire established their own bases but on Imperials, the bases there are very make-shift, the one you start in being the most entrenched. The bases occupied by Imperials on the Republic side, however, are intentionally being occupied to serve their own ends. Suitable landing sites are few; even assuming that the Imperials set it up on their own, they're there for practicality -- to mine the crystals and get them off-world. So... mining bases and airpads aside, you'd have satellite bases to hold ground against the Republic to keep them from preventing you from taking crystals. Would they have established bases elsewhere? ... sure, why not? More presence means more confusion for the Republic. Observation outposts from before the events of the game would make sense... but again, the stress is that it's pointed out there are few suitable landing sites.
Covert. Not feasible, but still possible.
... still, the end of it all? During the Cold War I'd stress that the Empire didn't establish presences on those planets for the simple reason that... they didn't need to. The lore, both from other texts and what's given in-game doesn't support the idea that they had a presence otherwise.
[/conjecture]
For Makeb;
Neither side have any presence on Makeb pre-RotHC with the one exception of an old, old, retired Imperial Intelligence Agent taking residence on one of the Mesas.
