I can only speak for Aruba.
At the time the kingdom consisted of the Netherlands, the Netherlands Antilles(Dutch Caribbean Islands) and Suriname.
Aruba was busy with its own independence movement culminating in a 1977 referendum. The options were to stay as part of the Netherlands Antilles(with Curaçao as the head of government) or to secede and become independent. It ended with a 95% vote in favor of the latter.
The Treaty of the Hague(1983) was signed and Aruba's independence was set for 1996. In 1986, Aruba gained its "status aparte" paving the way for its independence in 1996. It was now a constituent country alongside the Netherlands Antilles and the Netherlands in the kingdom of the Netherlands.
The reason Aruba never ended up gaining full independence is because in 1994, both the government of Aruba and the Netherlands came to an agreement that total independence wasn't necessary yet and that the status quo was acceptable. The kingdom would continue forward as it had done since 1986 with Aruba, the Netherlands Antilles and the Netherlands until 2010.
The independence clause still exists in the kingdom statutes, giving Aruba the right to independence if it so pleases following a new referendum and a 2/3 majority in parliament. Curaçao and Sint Maarten do not enjoy this clause. As of today, there is no reason to believe that the people want to be completely independent in contrast to the 1977 vote.
Sources:
[Statute for the Kingdom of the Netherlands](http://Artikel 58 Statuut voor het Koninkrijk der Nederlanden)