How does a dot matrix led driver know the voltage of an led?
The driver neither knows nor cares what voltage the LEDs require.  As others have said, LEDs are current controlled, not voltage.

The driver is constant current source.

It is designed to provide a set current rather than a set voltage.

It compares the output current to an internal reference, and raises or lowers its internal resistance until the output current is correct.

The driver doesn't know about the output voltage at all.  It doesn't measure it, and doesn't need to.

The voltage is a result of the controlled current, not its cause.

If you connect a resistor to the output instead of an LED, then you could use Ohm's law to find the resulting voltage:

E=I*R

Where E is voltage (in volts,) I is current (in amperes,) and R is resistance (in ohms.)

The same thing happens with your LED, except that LEDs are non-linear so you can't just use Ohm's law on them.