The succession was automatic, i believe the King of the Belgians and the Pope are the only two monarchs who do not succeed automatically once their predecessor dies/abdicates.
With the pope that is logical because a new pope is generally only selected/chosen after the sitting one has died.
In Belgium it's a quirk in the constitution that requires the heir to be sworn in to become king.
I believe it was automatic: as of 1890, the Nassau Family Pact applied. Accordingly, no female could succeed to the throne of the grand duchy as long as there were dynastic males around. King Willem III of the Netherlands actually tried to take action earlier, in order to acquire the throne of Luxembourg for his daughter. But Queen Emma talked him out of him, persuading him to abide by the terms of the Pact -- despite the fact that Luxembourg's parliament might have been willing to go along with the king.
The 1815 Congress of Vienna had given the grand duchy to the house of Nassau, the rules of which were to govern succession in Luxembourg. As the law was semi-Salicism, Wilhelmina was not in a position to inherit the throne. Later on, however, the daughters of Grand Duke Guillaume IV were -- or not, acording to the Merenborgs, a morganatic branch of the Nassaus.
Queen Emma was a half-niece of Duke Adolf of Nassau-Weilburg, and wanted to see him acquire a throne after he lost his during the 1866 war between Prussia and Austria. Her action may have been a blessing in disguise, because his own descendants ended up in a minor dispute over the grand ducal succession, when Prince Georg (a half-cousin of Grand Duke Guillaume IV) tried to assert his and his son's rights to the throne of Luxembourg, despite the fact that his father (Prince Nikolaos) had predeceased his older half-brother in 1905.
They lost, of course, thanks to the 1907 Family Statute (which they disputed). But the point that needs to be stressed is that it took a special measure on the part of the grand duke to ensure the succession of his own daughters, as it was not clear that he was necessarily the last agnate of the house of Nassau.
He was the last DYNASTIC male, thanks to the morganatic marriage of Nikolaos; but as one can see in the Russian and Saxon succession disputes today, morganauts often have a hard time in accepting their non-dynastic status.
When Wilelmina became queen, she gained a crown and lost a crown on the same day? She became Queen of the Netherlands, but lost out becoming Grand Duchess of Luxembourg when here father William III died? Did this happen the moment of his death or after when she formally accessed the throne of the Netherlands? Luxembourg has its own royal family independent of the House of Orange?