The TCR of a resistance alloy is produced by high heat treatment, generally a complex process to create a given TCR in a given alloy. Part of the problem for the alloy/wire manufacturer is that each ingot of alloy has slightly different characteristics so that the required heat treatment procedure is never exactly the same to get the same TCR, a really good metallurgist can minimize the unknown to some degree but it still something of a trial and error, if the 'finished' TCR is not achieved, it can be put back through the process again for another shot at the correct TCR. Tight control of the proportions of metal elements in the alloy makes for more consistency in the ingots but it is difficult to get much better than about 0.1% variation in metal contents.
For Evanohm, the heat treatment is far above the normal operating temperatures of even military resistors rated to operate to +125°C, in order to 'mess up' the TCR of an Evanohm alloy, you would have to raise the temperature well above 300°C, the top recommended operating temperature for Evanohm is in the range of 200°C and at this point the TCR is not the same as it is at +125°C. So as long as you don't get Evanohm really hot, the TCR will not change over time to any significant degree.
Mangain however is much more sensitive to temperature and any significant time of temperatures over 60°C can cause permanent changes to it. Therefore it is never a good idea to heat your Manganin resistor to anything over about 40°C-45°C for any length of time. Manganin is also sensitive to low temperature as well although it may be more of a temporary change than permanent if the temperature is not too cold or prolonged.
Another factor affecting what TCR is possible is the diameter of the drawn wire in Evanohm, the larger the wire diameter, the harder it is to achieve very low TCR, the smaller the diameter, the more comparatively easy it is to achieve low TCR and to some degree this depends on the ability of the wire manufacturer. Tighter low TCR specifications on the wire tends to produce higher wire costs, ask me how I know!
For the vast majority of precision wire wound resistor manufacturers, the end result TCR is not a tightly controlled end result, the TCR of wire can be affected by the manufacturing process of the resistor manufacturer because of various sources of stress, some of which are easier to mostly remove than others. Getting finished resistors with TCRs under ±1 PPM is not that easy and there is normally a variation in the end TCRs, how much depends on the manufacturer's processes. I should note that technically stress acting on a resistor's value does not actually change the wire's inherent TCR, it is still the same, the stress merely causes the apparent TCR to be larger than the real TCR, if it was 'relaxed' and freed of stress, the true TCR would appear again.