Vinegar will probably not set a purple dye of this day and age. It worked well for organic dyes in days past. Current dyes are almost always made chemically. To set them permanently, if you have a "bleeder" fabric, you can use Retayne.
Since you already cut out the pieces, I would simply take a piece of the purple and test it. Place it in a glass of water for several hours and watch to see if any purple streaking takes place (bleeding). After that, take it out and rub it against some of the white fabric to see if any dye transfers (crocking). It's also a good idea to rub some dry purple fabric against the white fabric to see if any dye transfers (dry crocking).
If the purple passes all of the above tests, I would go ahead and use it in the quilt. When washing for the first time, I would use Synthrapol along with color catchers -- just in case.