There is one shadow pool.
When the FP player plays cards, the twilight cost of those cards is added to the pool. When the FP player moves, twilight is added for the site's shadow number + the number of companions.
When the shadow player plays cards, the twilight cost of those cards is removed from the shadow pool. All shadow players have to share the twilight pool to pay for their stuff.
When the turn ends, all twilight is removed from the pool, the previous FP player becomes a shadow player, and the shadow player whose turn is next becomes the FP player.