What is a floor test?
Many people are unfamiliar with the floor test. I was too, but the Times of India lays out the process easily enough. In parliamentary systems, a government is formed from the parties represented in the legislature.
When one party has a majority this is easy - the chief minister is just chosen by the majority party.
However, when multiple parties are creating a coalition in order to form a government the issue is much trickier. The governor may ask for a vote of confidence in the coalition to prove they have the support necessary to form a government. This is called a floor test.
Why would a floor test occur after the oath has been administered?
A floor test is not required to become minister or form a government. The Indian Express reported that Palaniswami provided the governor with evidence that his party had decided that he should be Chief Minister. Since his party has a majority, it doesn't matter what the other parties think and he could be safely administered the oath of office.
A better question may be "why was there a floor test at all?". Although I don't have any specific knowledge of the Tamil Nadu legislature, generally confidence votes like this are a good tool for parties to formally show their disapproval as well as a way to root out dissenters in your party. The floor test is more likely a useful political tool, not an important part of the procedure in this case.