‘Independent’ is almost always misleading. People may call themselves independent, politically speaking but the vast majority of the time, that person actually has a marked political preference in his or her voting habits.
When a president is particularly unpopular, the number of independents will rise because voters of the president’s party feel a little embarrassed from the association and claim to be independent, but the basic leanings are not changed for most.
In this case, a NPR/Marist poll showing a seventeen percent drop in Trump’s approval rating is probably showing a segment of formerly GOP identifying voters now identifying as independent, with a significant, if not a majority, of those folks actually turning against the president. It probably also shows some Dem leaning folks who aren’t convinced that party has their act together, so while they are likely Democratic in their voting, won’t yet identify with the party.
This is terrible news for Trump and his party, but the real turning point won’t be until more people start identifying as Democratic.