From your description, I have one of those Channel Master four port distribution amps.
From my experience you get an equal amount of signal to each power regardless of how many devices are connected.
Also, it seems the amp only outputs to each port a signal very similar to what it is receiving on the input side.
In other words it outputs to each and every output port the same signal it receives on the input, whereas a splitter outputs whatever fraction it can divided among its outputs.
This device merely removes signal loss from the division of signal to 4 outputs and all are equally amplified up to the input signal regardless of how many are actually used.
Removing or adding a device has little effect on the signal to other ports.
Sorry the pic is upside down, this is my dist amp.