You choose whether to put a +1/+1 counter on the creature or create a Servo token as the fabricate ability is resolving. No player may take actions between the time you choose and the time that a counter is added or a token is created.

Fabricate doesn't cause the creature with the ability to enter the battlefield with +1/+1 counters already on it. For example, Marionette Apprentice will enter the battlefield as a 1/2 creature, then its fabricate ability goes on the stack. Players may take actions (such as casting instants) while the ability is waiting to resolve.

If you can't put a +1/+1 counter on the creature for any reason as fabricate resolves (for instance, if it's no longer on the battlefield), you just create a Servo token.