Sprouting and turning green are two basically unrelated things.
Sprouting means the tuber tries to form roots and grow into a new plant. It can be triggered by light, but even more so by warmth and the "internal clock" of the potato. That's the reason you are supposed to store potatoes in a cool place, ideally around 10C / 50F.
And yes, the sprouts contain solanine, but as they are not eaten and sprouting does not significantly raise the solanine content, sprouting per se is not critical.
(The reason gardeners encourage sprouting in light is the fact that the sprouts remain shorter, less brittle and some even grow the first tiny leaves.)
Greening, on the other hand, happens whenever a tuber is exposed to light - even in those that are growing slightly partially above the soil, which means you can even harvest green potatoes, although they are typically not sold in stores. This greening correlates with locally higher levels of solanine, the glycoalcaloide found in members of the nightshade family and the rule is to cut off green parts. To prevent greening you are supposed to store potatoes in a dark place.
So while both effects may happen together, sprouting does not automatically mean greening.
If you look closely, you can sometimes see a green tinge that needs removing, e.g. here:
For the really dark purple varieties, it may be hard to impossble to see clearly. In these cases, a bit of knowledge about solanine distribution in green potatoes helps: the highest concentration is found in the green parts of the skin and directly (as in one or two mm) below. So if you suspect exposure to UV light, peeling those potatoes should bring you easily into into safe territory - reducing the solanine content by up to 80%.
And finally, note that solanine is a rather weak poison. Sources vary a bit, but typically you find doses of 2-5 mg/kg body weight for toxic symptoms. Modern potatoes contain around 7mg/kg in and directly below the skin, way less in the other parts. Heirloom breeds can contain significantly more, but I couldn't find exact numbers, again, peeling removes a significant portion. And the last line of defense is your palate: Solanine tastes slightly bitter, so eating bitter potatoes is a bad idea, both from a culinary and from a food safety position.
In short: no need to worry about your sprouting purple potatoes if some basic precautions are taken.