Nassau was not just a place, it was also a noble house, and had marital and dynastic ties to the house of Orange, hence the Principality of Orange-Nassau. In 1815 though Willem IV traded Nassau with Prussia for Luxembourg, and it was then ceded to the independant Duchy of Nassau.
Therefore, the two Nassau battalions at Waterloo were under Wellington's command, but not as part of the Netherlands' armies, they were simply post-Confederation anti-Bonapartist forces - contributing to the Seventh Coalition. Their commander, von Kruse, had actually fought against Wellington's forces before in Spain from his time in the Confederation of the Rhine, but they could apparently put the past behind them for the sake of the present.