The choice of creature type is made as Adaptive Automaton enters. Players can't take any actions between the time the choice is made and the time the appropriate creatures begin to get +1/+1.

You must choose an existing creature type, such as Human or Warrior. Card types such as artifact and supertypes such as legendary can't be chosen.

Even though Adaptive Automaton is a Construct, other Construct creatures you control won't get +1/+1 unless you chose Construct as Adaptive Automaton entered the battlefield.