I bought a used Sigma 10-20mm f/3.5 EX DC HSM and I'm having some concerns regarding the autofocus. While it focuses quickly (tested on my Canon EOS 80D), it does so quite loudly and abruptly. That is, instead of a smooth focus transition, it jumps between points which produces an audible clattering noise. I'm not sure if this is expected or a defect. I read multiple reviews and all of them said the autofocus works without making much noise, as seen in this video (2:53). My lens autofocuses more like shown in this video. The focus distance will jump a couple of times, giving off an audible clatter, before settling on the correct focus. This happens both with phase detection and contrast detection (Live View). Manual focus is completely quiet though, so I believe the noise is caused not by some defect in the lens but is just mechanical noise caused by the quick focus jumps.
Is this in fact a defect? And if so, is it likely that this defect only occurs with this specific combination of lens and camera? (I am wondering if the seller knew about this or if he might not have had the same problem.)
Also, if I can live with the noise, is it wise to keep the lens? As in, will this cause additional problems/damage to the lens in the long run?