Her power has brainwashed them, making them to listen what she has to say. This power didn't affect the main party members.

The main party members (except Rinoa) were not in the radius of the audience's location in the first place, which means they weren't affected by Ultimecia's brainwashing power.

The guests, Ultimecia and Rinoa all were in the radius. When Ultimecia shows up, she has casted a spell on them (everybody in the radius), making them brainwashed before beginning her speech. After she casted a spell on them, Squall rushed into the audience and the speech has just started. Rinoa was in the radius before Squall shows up and therefore she was also affected by the power. Ultimecia cannot possesses two persons (Edea and Rinoa) at the same time, so therefore she was possessing Edea and Rinoa/along the guests were being brainwashed.

Oh, after she has casted her brainwashing power before beginning her speech, it doesn't mean that a new person (e.g. Squall) gets into the radius will become brainwashed. Which explains why the party members (e.g. Squall and Irvine) didn't get affected when they went into the radius AFTER Ultimecia casted the spell.