Does the architectural style of your home determine your design style? 

Yes, to some degree.  While some styles, like the ubiquitous late 20^th century construction colonial can handle an eclectic approach, some look plain silly when the period is not addressed inside.  It is hard to imagine Victorian wallpaper inside a Spanish Revival House.  Or Midcentury furniture in a Tudor.

Thankfully, most people are drawn to a time period, and so their construction choice is often harmonious with their furnishings and accessories.   The type of person drawn to a high rise condo feels complete with a minimal contemporary scene.  Someone who buys an Arts and Crafts home probably appreciates rich woods. 

Certainly some mixing can occur.  Post-War Construction style homes, from the Rambler to the Split-Level, can handle Midcentury Modern as easily as Country.  A Cape Cod need not have Colonial furnishings.  The trick is to recognize and pay homage to the period in which the style was created, and move forward into today by added items that are personally meaningful.