Most passive components with different tolerances, like resistors, thermistors, capacitors, etc, are all made on the same assembly line, using the exact same process. Then they are assigned to tolerance bins based on their measured, at room temperature, value.
Lets say you have a nominal 10 Kohm resistor. Those with values within 10 ohms of 10 K are labeled 0.1% parts. Those with values outside that range but within 100 ohms of 10 K are labeled 1% parts, and the remainder go into the 5% or 10% bucket. The components with the values closer to the nominal command higher prices.
Since all these parts come off the same manufacturing line using the same process, I would expect that parametric variations such as aging or temperature caused changes would be pretty close to the same.
You mentioned "quality" in your question. That's somewhat different than the initial tolerance. Parts destined for hi-rel applications like aerospace or space generally have a lot more paperwork, inspections, maybe lot testing, etc involved to guarantee their performance in those rigorous environments and long life times, which may be 20 years, 25 years, or more from design through deployment and end of life. A lot different than a typical consumer product.