The Text style uses
FontFamily->"Times". Your fonts are almost certainly set to have the same family name as the built-in font that Mathematica normally uses, and leaves the system with two possible sets of fonts to choose from. Even though the internal font name being used is, e.g., Times-RomanSC, that's not the actual family name...that's the style name (I'm not sure how standard the term "style name" is, but it's the term that FontLab uses for this).
As a result, Mathematica asks for "Times", and this font shows up in the list of candidates. Mathematica will choose the first font the system offers from that list. I would have expected Mathematica to understand that this is a small caps variant, and not use the font unless you wanted small caps, but it's entirely possible that the variant information in the font is not declared in a way that Mac OS X recognizes, probably due to it using older, Type 1 technology. I wouldn't be surprised if other applications on your system have similar problems.
If you could edit your small caps fonts to change the font family name, that would certainly fix things. This isn't about the filenames being used by the font...this is about the inherent family name set as a property of the font itself. You'll probably need to change the style name to match as well.
Otherwise, you could use the Format->Show Fonts menu item to see if it's possible to pick the correct Times font and, if so, determine what the properties are by looking at the underlying cell expression (Cell->Show Cell Expression). Armed with that information, an expert could help you figure out how to modify options/styles to avoid this.