atDNA (or "auDNA") is shorthand for autosomal DNA test.
To be considered reliable, you'd need to know if your matches are sharing the same chromosome segment and position. ancestry.com doesn't provide any chromosomal information unfortunately, rather it only provides segment lengths and counts so you can't know if a particular segment was mutually inherited by your matches (and thus much more likely to be attributed to the same ancestor).
edit to add: As you may already know, Thrulines is a double-edged sword. It can find potential ancestors, but if your matches have incorrect ancestors in their trees, then Thrulines has no problem whatsoever suggesting those incorrect ancestors as if they were also your ancestors.