This sounds to me like the kind of pseudo-scientific, or semi-scientific, language which is rife in the beauty industry, designed to impress the customer but possibly spurious.

I can only summarize what I have found in non-scientific sources; the validity of what is claimed can only be properly assessed, and the precise process explained, by someone with more scientific knowledge than I have.

I don't know whether something has been lost in translation here, but "ionic reflection" is found in relation to a particular make of hair curler, called Sibel, manufactured by Ultron, and advertised here, for example, by Amazon:

"Sibel Professional Curl & Go Tourmaline 38mm Tourmaline Barrel with Ionic Reflection
http://www.amazon.co.uk/Sibel-Professional-Tourmaline-Barrel...

Ultron's own presentation of its "Gold Ceramic Curling Iron" refers to "negative ion reflection for improved hair softness and shine"
http://www.ultrononline.com/products.asp?pr=1670&rf=3471
Ultron is a German company and its original German presentation speaks of "Reflexion negativer Ionen".

An ion, as I recall from school, is an electrically charged particle, "an atom or molecule in which the total number of electrons is not equal to the total number of protons, giving it a net positive or negative electrical charge" ( http://en.wikipedia.org/wiki/Ion ). The negative ions, by all accounts, are the good ones from your hair's point of view. Allegedly they "reduce the size of the water molecules allowing moisture to penetrate the hair shaft"
http://www.elchimusa.com/pages/ionic.html

Here is another series of claims about what these wonderful negative ions do to your hair:
"Negative ions are atoms that can stop the growth of bacteria, fungi, etc., resulting in healthier hair and scalp. Negative ion energy is powerful enough to break apart clusters of water molecules. The smaller water molecules penetrate into the hair shaft by slipping between the cuticles, adding plumpness/volume to hair. The bombardment of negative ions also closes the hair cuticle, which is very good for the health and appearance of the hair"
http://www.flatironexperts.com/Metropolis-T-Ion-Tourmaline-C...

Whether all this is true is secondary. The point is that "ionic reflection" involves bombarding the hair with negatively-charged ions. Tourmaline is "a precious stone that generates a vast number of negative ions upon heating"
http://www.wisegeek.com/what-is-an-ionic-hair-straightener.h...

So this curling iron works by having an element which, when heated, emits a large number of negative ions. I do not understand the sense of "reflection", Perhaps the ions are somehow reflected and concentrated by the curling ion, but I suspect it simply means "emission".