The resistors in the 7->10V stage are critical from TC point of view, indeed.
In case you want, say, < +/-1ppm/C TC of the 10V ref, the "ratio TC" of the resistors has to be less than +/-0.5ppm/C (the LM399 itself is typically -0.5ppm/C). Their "ratio TC" applies because the 2 resistors create a "divider", thus the "absolute TC of the resistors" is not that critical, but their "ratio TC" or "matching TC" matters.
With "25ppm/C" resistors in that stage you may get anything between + or - 50ppm/C at the 10V output easily (+/-500uV/C).
I was using the LT5400 4x10k resistors (DS: "matching TC" 0.2ppm/C, absolute TC 8ppm/C) getting aprox 10.54V out, with 25ppm/C resistor in the 399 "cathode", and the overall TC was less than -0.6ppm/C with many 399's I tried.
The "long term stability" and the "voltage reference noise" are different topics, sure..