Required servo control current
Ideally the PWM input wire of a RC servo would never sink or source any current, it would have infinite impedance. The signal input of a real world servo can draw or source some current and will have a certain amount of capacitance to ground and the power supply (the magnitudes depend on the design choices of each particular servo), but these parasitic effects are neglible in practice.  

It is safe to assume that you can drive a servo directly from an output of an ATtiny. Most ATtiny chips can source or sink 20 mA, which is orders of magnitude more than the signal pin will ever draw. If you are still paranoid you can add a 280 ohm current limiting resistor between the servo signal input and the microcontroller pin.