Triggers Priority When multiple cards from different places trigger their effects at the same time, the priority order - unless said otherwise - is: Creatures (from first position to last) → Supports (from oldest to newest) → Hand (from oldest to newest) → Graveyard (from oldest to newest) → Exile (from oldest to newest).
Creature get trigger priority from bottom up starting with the active players creatures and then the other players creatures. So during your opponents turn all of their creatures have higher priority and would trigger their enter the battle effects before your Thalia triggers. Supports have lower priority than creatures so it's the same situation. Your opponent's creature with an enter the battlefield effect will trigger before authority of the consuls does. Or least that's the default rule for how it's supposed to work unless the card says otherwise.