The strategy of the two hybrid system is to separate the two domain of the activator encoded by GAL4, making activation of a reporter gene impossible. Each domain is connected to a different protein.
Similarly, if the two proteins interact, they will join two domains together. Then the activator will become active and start transcription of the reporter gene.
The bait proteins fused to the GAL 4 DNA binding protein do not activate reporter-gene expression. This is because they do not contain activation domains. If bait activated transcription on its own the assay would not work.