Birds get mites.... I haven't heard of them getting live or mites though.
I would suggest you have the a-vet or their assistant show you how to medicate your tiels when you go to pick up the meds. Also, ask them how to feed the meds if your tiels wont accept it!
Flavoring the meds can help, but sometimes it helps to mix the meds into yogurt, organic fruit juice, put it on bread or mix with treats, mix with honey, etc.
When I give meds or supplements, I have the bird sitting in my lap as I retrain their heads and simultaneously open their beaks using my left hand. I then slowly squirt the medications from the syringe into their mouth and allow them to swallow before giving them the rest. Some people find it easier to wrap birds in a towel/washcloth so the birds don't flail around, however I have found that the birds may become overheated this way.
It is best to have your a-vet show you, but it may also help to read about it... so here's a few articles and a video!
Medicating Pet Birds Orally
How to Medicate Your Bird - Page 1
[ame=http://www.youtube.com/watch?v=DVvyy75JFZE]Pet Care's Dr. Poutous Shows How to Medicate a Pet Bird - YouTube[/ame]
Free e-book on medication parrots! Would definitely recommend this! It's a link to a blog, which has a direct link to the e-Book (sample) on medicating parrots! When you get to the page, it says the e-Book is $19.95. Click on "Buy Now" and enter the promo code
PARROTRX!!!! Haven't gotten it myself, but definitely going to get it!
Good Bird Inc Parrot Training Talk: Medicating Your Parrot
And a little humor about medicating parrots!
Winged Wisdom Pet Bird Magazine - Medicating Parrots (A Bit of Humor)