Why doesn’t a spectrometer show a dramatic spectrum change when measuring a colored card under tungsten light?

A colored card usually does not emit a single “red” or “blue” wavelength. It reflects a broad spectrum, but with some wavelengths favored and others reduced. Under tungsten light, the reflected spectrum is therefore still largely the tungsten source spectrum, shaped by the card’s reflectance curve. Those relatively small spectral differences are enough for our vision to perceive strong color differences.

Also, your meter likely has a very wide acceptance angle (an integrating sphere can approach 180°), so even held close to the card it may still collect some surrounding light. A blackened tube or snoot over the sensor opening could help restrict what it sees.

So the main reasons are:

1. object color comes from selective reflectance, not usually a single narrow spike, and
2. the measured spectrum is the source spectrum modified by the material’s reflectance and geometry, not replaced by a pure object color.

In short: the meter is behaving plausibly. The card slightly reshapes the tungsten spectrum, and those slight changes are what appear as strong color to human vision.