Air carrier flight crew reported while on a visual approach they made an unstable approach resulting in ATC issuing a low altitude alert. The flight crew landed safely at the airport.

Narrative

We saw ZZZ was landing XX due to winds; a rare airport configuration and we selected the wrong approach.During the flight I noticed I had missed a few radio calls; uncharacteristic for me (now believing this to being a sign of fatigue); I had done the stadium visual previously. The PF briefed the arrival; planning flaps 40 on landing.On while on approach; glide path and lateral nav were locked in until the tower controller announced in a stern voice we were too far east and to correct immediately; as we began to turn tighter towards the airport on base we quickly got a low altitude alert from atc which confused me as we were on centerline horizontally and vertically of the approach. Path was safely adjusted after I verified we were clear of terrain by looking outside and confirmation of obstacles/terrain alt on the Navigation Display (ND). I was distracted by fatigue and the mental task load of went wrong a minute ago. The PF had his hands full with a very busy approach in very gusty/turbulent conditions with winds 300@28G40. We conducted a stable approach with flaps 30 instead of flaps 40; recognized it late; and configured below stable approach mins; at the same time ATC asked us to expedite at the same time; we then executed a safe landing.