After our last game I am still not 100 percent sure what is allowed when you activate a system. For example.
If I activate a system during my tactical turn and decide to build in that system, then when my turn comes around again in the same round and phase, am I allowed to build again in that system i activated already even though it wasn't activated that turn?
If so please show me where it is in the manual as I have looked everywhere
The normal build-time comes as the last step of the tactical action. Thus, building in a system requires you to activate the system in question. And since you only can activate non-activated systems there is, in general, a "one build per system" limit.
Certain circumstances (i.e. strategy cards) allow you to build in a system that is already activated though. They are, off the top of my head, the Imperial and Imperial II secondaries, the Production primary and the Industry Primary. The latter is only used in the "Fall of the Empire" scenario from Shards of the Throne.