Taking in a couple birds

I don’t know how to start this but we’ve taken in a couple of birds (gold capped conure, monk, and Galah). I don’t have all the time in the world. I work full time and have 4 kids. However I can provide a safe environment, great food, vet visits, toys, nice cage. The only thing I’m lacking is time to tame these guys. Will they live a good life without becoming one of those parrots that hang out on their owners shoulders?

I have parrot experience, I hand fed my Mexican Amazon and mitred conure, and I have a pair of cockatiels that are my daughters’ and they’re delightfully sweet and the kind where they can ride on your shoulder all day and like to give kisses and cuddles.