If yours are now 8 years old and haven't raised any clutches, chances are they won't (which is good for someone not into breeding).
Anyone who colony-breeds tiels (as the person where you bought your birds did), there is going to be a certain amount of inbreeding take place, and usually it's a lot of inbreeding if original flock and their offspring are kept together for some time. In colony breeding, one never knows for sure which males fathered which chicks (some of those females are little jezebels that breed with several males).
When I was breeding cockatiels, it was for purposes other-than making babies. I was working with triple and quadruple mutations (whitefaced cinnamon pearl-pieds) and kept detailed pedigrees on all the birds.
I kept all my non-breeding adults in separate flights, males in one, females in another, and then *I* chose which two birds were to be paired up. That way I knew with certainty who the parents were.
After their breeding duties were finished; they were put back in their respective non-breeding flights.
Sometimes I used the same male with another female. One male of my original stock, was extremely nice so I kept him busy with many females, with a week or two rest before pairing him up with another female.
And sometimes I "intentionally" inbred for certain qualities, traits, colors and achieved my goals without compromising the genetic health of the chicks.
When inbreeding, you're doubling up on both the good genes as well as the bad genes, so if there's any genetic problems they will come out. But both parents must be carrying the same genetic weakness to show up. Inbreeding doesn't cause freaks, and it doesn't automatically cause liver or kidney problems in offspring.
Carefully planned linebreeding/inbreeding by knowledgeable folk is fine; colony inbreeding isn't.