If a spell caster takes damage, to temporary hit points only, the damage doesn't "spill" over to "real" hit points, while concentrating on a spell is a concentration check required?

Yes, because concentration is specific on when you take damage, not when you lose hit points. 

players handbook pg 198  "Temporary hit points aren't actual hit points: they are a buffer against damage, a pool of hit points that protect you from injury"  So if temporary hit points are a buffer against damage how is it that I have taken damage when in fact I haven't?

They prevent damage to you, your physical form, but you still take damage, just not to your normal hit points. It is still damage, you still make concentration checks, but you don't take damage to your normal hit points.

ok. I'll buy that explanation.  Thanks

Think of it like Wild Shape. While wild shaped, you get extra hit points. You can concentrate on a spell while in the beast form, and you have to make concentration saving throws still while wild shaped. If you don't have to make concentration checks while wild shaped, that would be broken, way too powerful. The temporary hit points give you a bit of extra hit points that can help you not die just a bit more, but it doesn't make you feel pain less. It gives you a small boost of health, but it doesn't cause immunity to the damage you take from a spell or weapon. 

Temp hit points still count as damage and you take concentration checks when you take damage.

To my knowledge, the only thing that stops the concentration check is the Abjuror wizard's Arcane Ward.  That stops actual damage.

https://rpg.stackexchange.com/questions/55609/is-a-concentration-check-required-when-temporary-hit-points-absorb-all-the-damag