The Animate Objects spell indicates that the objects act on their turn, but it doesn’t explicitly state what their initiative is. Are they supposed to roll initiative using their Dex modifiers (either individually or with their size class)? This would be as in the Find Familiar spell:
In combat, it rolls its own initiative and acts on its own turn.
Or do they act immediately after the caster? This would be as in the Summon Beast spell:
In combat, the creature shares your initiative count, but it takes its turn immediately after yours.
Or does this simply require a decision by the DM?