... This is the current required to energize the relay. The opto-isolator's transistor will see this current. The Arduino control current will be 15-20mA through each control input (IN1-IN4).
Although I fully agree with the fact that the board requires separate power supply (Arduino power supply would not be able to energize all relays), the optoisolator driving current will be much smaller than 15-20 mA.
Each relay control input, connected to Arduino control output, is active low, that means it must be connected to ground to activate the relay. However, Arduino output voltage at low level is not 0V, Atmel ATmega328P datasheet shows Vol voltage (voltage on output pin set to "0") at sink current below 10mA being approx 0.6 V.
The control current runs from Vcc voltage through 1kohm limiting resistor, through optoisolator LED and through red indicator LED to control input (which is ~ 0.6 V in active low state). Voltage drop on 817 optoisolator LED is approx. 1.2V, voltage drop on red SMD indicator LED (in series with optoisolator) is around 1.8 V. When connected to +5.0 V power supply, voltage on 1kohm limiting resitor will be around 1.4 V (5.0 - 1.2 - 1.8 - 0.6), resulting in 1.5 mA sink current from each control input