When the Netherland and Belgium were ruled by Spain, were the people there Spanish citizens/subjects?

Citizens, no, at that time the term only applied to people living in cities. There was no institution of citizenship as we know it today.

They were subjects of the king of Spain, simply because a subject is someone who is underneath the authority of a king. To illustrate what I mean someone from the UK and Canada are subjects to the same monarch, but aren't citizens of the same country.

To refer to the Spanish Netherlands as a province of the Spanish Empire is not legally correct, since it was only linked to Spain through a personal union, it had it's own institutions, and was ruled indirectly, through a representative of the Spanish monarch. The institutions I referred to existed prior to and after the Spanish rule. They didn't interfere much.

Spain's King Carlos I was Flemish, born in Ghent.

Charles V (24 February 1500 – 21 September 1558) was ruler of the Holy Roman Empire from 1519 and, as Charles I, of the Spanish Empire from 1516 until his voluntary abdication in favor of his younger brother Ferdinand I as Holy Roman Emperor and his son Philip II as King of Spain in 1556.

http://en.wikipedia.org/wiki/Charles_V,_Holy_Roman...

Those lands might've been under the same flag as the Spanish Empire for a while, but that didn't all of a sudden make the people Spanish -- in the same way that the Flemish didn't become French or Austrian when Flanders was part of the French or Austrian empires. It was not a province of Spain (or a colony as some Spanish trolls like to insinuate from time to time), but it was part of the same realm and under the same ruler.

Spanish subjects - the area was known as the Spanish Netherlands,and was a province of the Spanish empire.