Reason being is that once inside the helmet, light is only allowed to pass through the lens in one direction and the dark interior does not let it reflect out.
This is physically incorrect on two counts: 1) The lenses are not polarized, so light travels with equal power through the lens whether from direct or indirect (reflected) illumination. 2) As for the dark interior, with a human head in the helmet, it is not a dark interior any longer. The reflectance value for human skin is not extremely high, but certainly high enough to make a pronounced impact photometrically on surrounding objects or transmissives.
Amber (yellow) and red occupy very different wavelengths of the spectrum, and one can not "convert" into another without some particular things going on in the material substrata. This is absolutely possible - for example, some thin coatings can produce what is known as "interference" causing a host of other spectrum colors to appear, but we'd need to confirm such was the case with the lenses.
We need to know why this color shift would be happening, because the whole "reflected light" thing has nothing to do with it, from a physics standpoint. Neither does the presence of a lower-reflectance area behind the lenses - if anything such a thing would reduce perceived saturation of the lenses, not intensify it, and certainly not change its spectrum. Consider yellow tinted sunglasses. You can see the yellow coloring much more clearly against a white background than a black background, because the higher reflectance of the white background reflects more illuminant energy back through the lenses.
Do you know what the lenses are made of? I can do a quick IOR table lookup to see what its photometric properties are.
_Mike