Welcome to the forums and the ever exciting world of budgie ownership!
You have certainly come to the right place as you will find all you need to know on budgie care here.
Since you are new to budgies, the information on the several articles and sticky threads located at the top of each section of the forums will be extremely useful as you become more familiar with the species.
Considering it's only been two weeks since you had your budgies and they may still be in the process of fully settling in, it seems you are having positive results with your approach in training. The key truly is to take things slow, to read the budgies' body language and respect the safe boundaries set by them when we are interacting more closely with them.
With time, the foundations of trust will be established and with continued work the bond you have with your budgies will solidify.
Be sure to check the info and tips on this subject here at the top of the page of Taming and Bonding section.
Onto your question, it's true that in very specific situations where we need to hold a pet bird to administer medicine that there can be a little setback in the trust the pet bird has for us, but this can be easily overcome by continuing to spend quality time with the pet bird and by making use of the training techniques. The deeper the bond you have with the pet bird, the sooner they will forgive the handling/grabbing.
This link may be of use if you haven't already read it: https://talkbudgies.com/your-budgies-...ng-budgie.html
The work to keep up the trusting bond and friendship with the pet bird doesn't really end, this is something that is maintained by the daily interactions we have with them. The way I see it, the training never really ends no matter how deep the bond we already have with a said pet.
Also in case you don't know, it's best to not use mite sprays because when spraying, the product can hit eyes and there is also the chance of ingestion of the product.
It's simpler and more effective to use a spot on treatment where you apply a drop of the product on the back of the neck and directly into the skin.