I have 3 Pokemon on my Bench, and 1 of them has the "Omega Barrier" Ancient Trait. My opponent plays Cyrus {*}, and I choose to keep the 2 Pokemon that don't have "Omega Barrier". Does the Pokemon with "Omega Barrier" get shuffled into my deck?
Yes, it does. The effect of Cyrus {*} is on the player, not on the Pokemon with Omega Barrier.
Source: TPCi Rules Team (2018-05-31)

Relevant cards

Note: All applicable cards may not be listed below.
SM5_120
XY5_151
XY5_24
XY5_60
XY5_77
XY5_86
XY5_9
XYP_XY49
XYP_XY49