The mapping updates the osm database immediately but the rendering of the map takes longer, with the standard layer sometimes taking a few minutes to a day or so. Refreshing or clearing the cache on your browser may help (control+r for me and control+ f5 for some). Other upstream caches may be the cause delays - my phone takes a very long time even after clearing the cache.
Another way to see the latest is to copy the url from your browser and paste in a tor browser which is unlikely to be caching part of the map tiles for your area.