From checking into this device it looks like it uses a small step-up transformer.
If so, the boost is real, not perceived. However, it is a voltage boost, not a total power boost. Because power (watts) can be expressed as EMF (volts) times current (amps), if a transformer boosts the voltage, the current must go down. The transformer isn’t creating anything; it can be thought of as just transforming the power.
For example, if a transformer doubles the voltage, it will necessarily halve the current. But, the power remains the same. If I have 2 volts at 2 amps, the total power is 4 Watts. If I have 4 volts at 1 amp, I still have a total power output of 4 watts.
In the situation of the booster you installed, the little device probably is transforming the signal to boost the voltage. The current of that signal is being reduced, however. There is no “free lunch”, as they say.
Nevertheless, since the circuits our guitars immediately touch are more voltage sensitive, and have a very low current draw, the reduced current capability is of less concern than the increased voltage.