Yes the purple are the air disappearing. Depending on the humidity, I have had the lines disappear in minutes, not hours.
The purple pens are best used for marking as you go. Better suited to LA and hand quilting. I have also used them to mark embroidery lines.
The blue water soluble pens are the ones that last a bit longer but you don't want to leave them on too long. A week or two at most.
Both products should not be ironed over until the quilt is thoroughly washed to ensure all marks have come out. Heat sets the marks.
There are also the frixion pens that you need to hit with steam or heat to remove but they can return if the quilt is exposed to very cold temps (such as in the back seat of a car during winter) until it has also been laundered. There has also been reports of the frixion pens fading dark colored fabrics.