When he/she picked Brave Bird and Lucario picked Quick Attack It had Talonflame going first instead of Lucario. It looked like a glitch to me.
It's because the Talonflame had the ability gale wings in which makes flying type moves have +1 priority, and the Talonflame probably had a higher speed so brave bird went first. Hope I helped!
Source: I have a gale wings Talonflame
does your Talonflame have Gale Wings? if so it gets a +1 priority on Flying moves (Brave Bird) and so it would outspeed almost anything