Well, I guess you will have 2 positions for your servo, a position for the platform down and a position for the platform up. Let's assume the first position is the servo arm at 0 degrees and the second position is the servos arm at 90 degrees. When you apply power to the servos and electronics, the servo will jolt until a signal will tell it to go to the first position. So, when you set the servo active, before you enter the main code, write the first servo position to the servo. That will make the platform go to the Down position. If you use a hardware PWM signal, the servo will keep that position until you tell it to go to another position or you take the power off, or deactivate the servo (WebbotLib will do just that).
To keep the servo from moving when power is applied, you will need to apply the signal first, then turn ON the servo power. You can do that if you use a relay to apply the power to the servo, or by having separate power supplies for servos and electronics and switch the electronics power ON first, then the servo power.