We do get exactly 50% of our autosomal DNA from each parent. However, beyond them, the actual amount we inherit can and does fluctuate from the expected average.
For the "genetic ethnicity" portion on Ancestry's test, technically called a bio-geographical ancestry (BGA) analysis, we're not talking 10s of generations, but 100s or even 1000s.
The analysis shouldn't take the online trees into account at all! I've seen plenty of shoddy, undocumented, or downright fabricated trees on here.