I would have thought regular on passage?
30 years ago there used to be only very small numbers of White Storks wintering in Iberia. The growth in open landfills with the associated junk food has meant there are now in excess of 15k:eek!: Presumably Black Storks now winter in small numbers.....
Wintering White Storks in the Algarve have increased in the last decades, true and partly due to (one!) landfill site, but not entirely because of this.
However Black Storks do not normally winter at all in the Algarve, in fact winter records are pretty rare. Nevertheless, some 10s winter in nearby Coto Doñana in Spain.
From an Algarve perspective, Black Stork is only seen regularly among the autumn raptor movements around the Sagres peninsula, in the far west. Numbers are either singles or single figures, with occasional groups in excess of 10 birds on one or two occasions through the whole migration period. Notably, these birds are not with White Storks, in fact WS is rare as a migrant in Sagres. These birds move high inland with the raptors and are rarely seen along the coast at wetlands. The site that the OP saw the bird is part of the Ria de Alvor wetlands, where its barely an annual visitor. The same is true across the Algarve wetlands, which are far from under-watched by the way! In fact most Algarve wetlands don't have Black Stork as even an annual visitor. Black Stork does breed however, albeit a tiny population just north of the Algarve.
Regarding rubbish tips; I think you are behind the times - most of the old open rubbish tips are closed down, though there is a modern one near Silves that attracts White Storks. The main reason for the increase in breeding birds in the last 20 odd years in Portugal (ongoing) is habitat protection and a reduction of nasties in the foodchain.
To regard the the cause of increase of breeding or wintering White Storks is due to rubbish tips, is a misconception