No, tests like that work with an abundance of DNA and so contamination is less likely. A DNA test typically works with saliva or blood which contains a ton of DNA> That DNA can then be amplified, which amplifies both the signal and the noise, but the noise is very low and can be trivially ignored after the fact.

With paleogenomics, you're collecting a tiny amount of DNA, mostly degraded, from ancient samples, and so the "noise" (contamination DNA) ends up being close to or more than the signal you get from the sample.

Details here: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3926038/