That adapter is hopelessly inadequate to the job: even micro-sized servos are likely to overload it.
It's always a good idea to power motors from a separate supply: they generate a lot of electrical noise that can cause reliability problems, and big ones are likely to overtax the Arduino's onboard voltage regulator.
These days, you can get a 5V regulated power supply that's good for a couple of Amps for $10 or less. I recommend doing that, and wiring up the servos with their own supply. Especially if they're going to be doing any heavy lifting or spinning.
Be sure it's a regulated supply: the really cheap ones will put out a voltage much higher than the nominal one if they're not fully-loaded, and might damage the servo electronics.