If there's more than one work on a line when you are hyphenating it's possible that the text is set with non-breaking spaces, but if all the spaces are non-breaking your column would have to be wide enought to hold the entire paragraph in one line so ther are probably some regular spaces someplace.
In any event, what you see is the result of ID not being able to find a place to break the text within the width of the existing column. Non-breaking spaces and the use of No Break rather than turning off hyphenation (they are very different things) are probably the tow major causes, but I've seen cases where paragraph indents were too large and left no space for text, or the specified font was too big to fit, and it's even possible that it's some sort of Keep Options issue.
The best way to find out is to open the story in Story Editor so you can see it all and show non-printing characters. Look for non-breaking spaces (fixed-width spaces don't break, either), and check the first word of overset text for No Break. If that doesn't find it, dig deeper in the paragraph attributes.
If you use relatively large type for your column widths, hyphenation is generally a fact of life for good-looking text with nice spacing. The fewer characters will fit the width, the more likely you will need to hyphenate.