If they add just a few more pet food (say, 3/week, as suggested), you will still feed the same pets (fire phoenix, brown bear, polar bear, twilight phoenix if you go far enough in tourney to make it worth feeding). Other pets would be fed only if there would be much more pet food than useful pets can consume.
You could occasionally feed some of the other pets, just to give yourself a treat, instead of cycling over the same ones.
Also, like I said, right now, feeding the fire phoenix each tournament can be complicated at first. I try to conserve pet foods and I look at the academy regularly, yet on my most advanced city, I'm barely at a stock of 20 pet foods, and that does go down real quick if I'm busy at work for a few days/weeks.