Captive Audience vs. Teferi's Time Twist
That ability on Captive Audience is a replacement effect that modifies how it enters the battlefield. Effects like this are described in the replacement effects section of the rules:

614.1d Continuous effects that read “[This permanent] enters the battlefield . . .” or “[Objects] enter the battlefield . . .” are replacement effects.
614.12. Some replacement effects modify how a permanent enters the battlefield. (See rules 614.1c–d.) [...]

When you exiled it and then brought it back, it would have entered the battlefield under the control of its owner, your opponent, but the replacement effect modified that so that it entered the battlefield under your control instead.