Here is a quick graphical outline of minimum and non-minimum phase speaker systems:

Start with a total system response from 20 Hz to 25 KHz…

This system is minimum phase...

All the rotation of the phase is a result of the roll-off at the ends of the response

Here is the response of a low-frequency driver with filter:

This reponse is also minimum phase...

There is addition phase rotation around 1KHz from the added lowpass filter

Here is the response of high-frequency driver:

This reponse is also minimum phase...

Here there is also an additional phase rotation around 1KHz from the added highpass filter

Here is the total combined acoustic response of low and high-frequency driver:

This reponse is NOT minimum phase...

There is still an additional phase rotation around 1KHz from the crossover...

But the summed frequency response looks just like the original system reponse

Except there is now an additional phase rotation, which makes the combined result not minimum phase

Finally, Here are what the two impulse responses look like - for the two systems: