Color meters vrs gray cards

[Juan]

Hi,
I just purchased a Sekonic C-500R color meter and to my surprise its
measurement of the incident light (in very controlled studio
conditions) temperature differs from what I get sampling the neutral
patches of ColorChecker in LightRoom or ACR 5.5.

So, which temperature should I use? And, aren't the neutral patches
supposed to reflect all frequencies in the exact proportion that it
receives them?

Finally, if there is a non zero CC to accompany the temperature, does
anyone know how the CC indexes correlate to Tint units in ACR?

Thanks,
Juan Dent