If you read the additional notes on that website
Additional Notes:
This circuit is just a basic one and can be used to test servos, or as a project interface for other enhancements. With the above component values, the circuit can drive a servo through a 90-degree rotation. The pulse is 1-mS wide, plus or minus 0.5 mS. Q1 inverts the signal from the LM555's pin 3. To get a 180-degree rotation the values of R1, P2, and C1 should be changed to 5K6, 560Ohm and 2uF respectively. R3 accounts for shift variations in the different variety of servo motors.
it seems that its sending a 0.5ms - 1.5ms pulse. The normal protocol is 1ms - 2m with 1.5ms being centre stick. So that circiut is not offering the range that the ESC is probably expecting. Best advice, scrap it and build Alain's suggestion as per the previous thread.

PS - you might be better off posting this sort of topic on a dedicated model electronics forum such as http://www.rcgroups.com/diy-electronics-199/ as this is really a PICBasic forum