Should drivers enter the crosswalk when pedestrians are crossing?

Hi,

A driver turned and entered a crosswalk as I was crossing in my residential neighborhood with my 3 kids, 1 of whom was in her stroller.

Shouldn't the driver have waited till we had finished crossing before entering said crosswalk?

Is there a legal requirement that the driver do so?

I called the driver out, who asserted that he had entered 'behind us' after we had finished crossing that segment of the crosswalk.

Who was/is in the right? The incident in question transpired in Fort Bend County.