Eating just seeds is not healthy for either bird. I don't know much about cockatiels, but I have two parakeets, have done plenty of research, and asked my vet about their diet.
Fresh veggies is a must, as well as fruit (but not as much as veggies). Think of it like this; in the wild, they're eating all kinds of fruits and veggies, not nothing but seeds and pellets. My vet, as well as many others, agree that two tablespoons of seeds a day is the max. Too many seeds can lead to the bird being unhealthy and even cause premature death, if that's ALL they're eating.
However, also research if a fruit of veggie is okay for them to eat. I know avocados will kill, and lemons aren't good for them, either. Apple seeds also aren't good.
If you need to slowly transition them into eating other things, that's fine. I'm currently doing the same (my budgies don't eat as many fruits and veggies as I'd like, since they prefer pellets, but I sprinkle some pellets on the food to get them to eat it). You can mashup the pellets and seeds together, since if you just mix it in, they'll just pick out the seeds and leave the rest.