Airiness in tone is usually caused by improper lip position and lip plate position.

Lip plate:

Are they using the "kiss and roll" method? That will pretty much guarantee airy tone. Kids tend to not roll out far enough meaning they will underblow - causing an airy, not full tone.

If they roll out TOO far, they have to overblow - similar issue, but airy the OTHER way.

So go back to HJ+mirrors - set the tone hole properly, and watch and reinforce it.

That being said, lip position can be an issue too. Many young students use an unfocused aperture and unfocused lip corners, causing weak tone.

Sir James Galway came to TMEA a few years (good lord, probably a decade or more now) back, and said his trick to teach good flute embouchure was to put the bottom lip OVER the top lip, then relax it until it fell open to blow through. This eliminates "smile" embouchure which causes poor flute tone. There are YT videos about it, but I've found it works wonders.