What height are you mowing it? It's possible that your rotary mower either cut the very top of the seedhead off and left the stem, allowing it to reproduce seed quicker, or it laid the stalks over and never really got rid of the seedhead. The sharp reel mower should take care of that easily, especially if you are mowing at 1/2" to 1".
Also, if Celebration is anything like Tif419, the seed production should slow way down once you get a little further into spring. Coming out of dormancy, it's the nature of the turf to try and reproduce as much as possible, and then it settles into its growth pattern as spring progresses. After mid-May, the only time we see any seedheads on our Tif419 yards is when they get extremely drought stressed and go into survival mode.