The game ends when the *first* player fulfills one of the winning conditions
Not according to the copy of the rules I'm looking at. From the last page of the rules that came with my Rio Grande edition, right before the Summary of Niagara section:
"As soon as a player has collected (in his play area) five different gems or four of the same color or any seven gems, he wins and ends the game. However, the current phase II continues until everyone has played. As such multiple winners are possible."(my italics on the last sentence).
My post edited a couple of times for clarity and to add the following: was there a snafu on some editions of the Rio Grande rules booklet? Why would Phase II continue after one player had achieved the winning conditions unless others could win?
My game also includes rules in French which state similarly: "Il est possible qu'il y ait plusiers gagnants". It's been a while since I studied French but to my mind that also says 'It's possible that there are multiple winners'.