The voltage regulator will take care of dropping the 11.1V down to the 5V needed for the microcontroller (although I don't know what regulator is used in the circuit, so look at the datasheet to be sure). The problem you will have is for the servos, depending on their voltage rating. You don't want to run the servos off the microcontroller power supply because you will run the risk of causing the mcu to reset each time a servo starts up from the initial power draw, if the servo backfeeds any current when it is stopped or reversed you run the risk of burning out your mcu, and (without looking back at the tutorial) I am pretty certain the voltage regulator used in the circuit can not handle the current draw needed for two servos.
You can either get servos rated for 12V, which you might already have, or create a seperate powersupply circuit using a higher amp rated and higher voltage output regulator. Either way, seperate battery is adviseable.