We measure the evolution of the quiescent fraction and quenching efficiency of satellites around star-forming and quiescent central galaxies with stellar mass $log(M_{mathrm{cen}}/M_{odot})>10.5$ at $0.3<z<2.5$. We combine imaging from three deep near-infrared-selected surveys (ZFOURGE/CANDELS, UDS, and UltraVISTA), which allows us to select a stellar-mass complete sample of satellites with $log(M_{mathrm{sat}}/M_{odot})>9.3$. Satellites for both star-forming and quiescent central galaxies have higher quiescent fractions compared to field galaxies matched in stellar mass at all redshifts. We also observe galactic conformity: satellites around quiescent centrals are more likely to be quenched compared to the satellites around star-forming centrals. In our sample, this conformity signal is significant at $gtrsim3sigma$ for $0.6<z<1.6$, whereas it is only weakly significant at $0.3<z<0.6$ and $1.6<z<2.5$. Therefore, conformity (and therefore satellite quenching) has been present for a significant fraction of the age of the universe. The satellite quenching efficiency increases with increasing stellar mass of the central, but does not appear to depend on the stellar mass of the satellite to the mass limit of our sample. When we compare the satellite quenching efficiency of star-forming centrals with stellar masses 0.2 dex higher than quiescent centrals (which should account for any difference in halo mass), the conformity signal decreases, but remains statistically significant at $0.6<z<0.9$. This is evidence that satellite quenching is connected to the star-formation properties of the central as well as to the mass of the halo. We discuss physical effects that may contribute to galactic conformity, and emphasize that they must allow for continued star-formation in the central galaxy even as the satellites are quenched.
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