Oooooooh, they're giving you their backs! I remember that!
When my bird used to do that I think he was letting me know it was time for me to leave him alone!
Are they in front of a mirror or is that a second cage and another bird behind them? If it's a mirror, move them now. Place their cage on a table up against a wall and make it so the perch where they sit is at least as high up as your eyes. Choose a spot where people are not going to be walking past the cage at very close distance, but don't put them away in a room where nobody goes either. When you do this you will be helping them feel that their cage is a relatively safe place to be. Birds feel safest when they can look down on you. Peel the skin off an apple and cut them a small slice, taking care to remove the seeds and the little area where the seeds sit in the apple. Apple seeds are bad for birds. Put the small slice in the cage, maybe clip it to the bars near the perch or cut it in bits and put it in the cup. Then go stand in the next room, put on your sunglasses, and spy from the doorway. You might (or might not) get to see them eat some apple, and that will make you feel better.
Congratulations on your very first pets! I don't want to scare you, but you have a lot to learn in a very short time. I do think that some other experiences in life can help prepare you for this, however.
Have you ever taken care of another living thing of any kind - a child, a fish, a hermit crab, a plant, helped someone else take care of their pet while they were away, or cared for someone who was very sick? Have you ever helped a friend when they were very unhappy or upset?
If you've done any of these, and you probably have done at least one or two, then you can draw on that experience to remember the kindness and compassion you needed to do that, and remember how you provided whatever that living creature needed, and how your actions affected them in important ways. I think of the skills of kindness, compassion, attention to detail, respect, willingness to learn, selflessness, patience, and diligence will take you a long way to success in keeping your pets. If you have those and you read up on some basic instructions for keeping birds, I think you will probably be fine.
I Googled to see if I could link you to bird keeping instructions for very beginners, but I was not satisfied with what I found. If you would like to let me know what you already have set up, I will see if I have any suggestions. Also, let us know what kind of routine you are developing for taking care of them. You should certainly check out the pictures section to see what others have done.
Here's a list of the bare minimum you need to keep them alive while you figure out what you're doing:
clean water in a dish you wash with soap every day and rinse very well
bird food they will eat - give them the same as they had at the pet shop while you are deciding how to feed them
big enough cage - big enough they could both flap their wings at the same time and not hit anything is the smallest cage you should ever put them in, but it really should be much larger than that
several perches of different diameters, made of WOOD
some bird toys - get those bigger than Budgie size but smaller than macaw size, and make sure they don't crowd the cage
change the paper on the bottom of the cage every day
keep the cage out of direct sunlight so they don't overheat
not in front of a window so they won't be scared by stuff outside
keep the cage out of drafts so they don't get chilled
protect them from physical contact with other animals or people who do not respect them
perches at human eye height or higher for their emotional comfort
natural day length - don't keep them up too late. They need quiet and dark for a good night's sleep of 10 hours or so.
Everybody - did I forget anything?
Talking about fast tracking their taming - please throw out any notion of rushing them. I am not so sure you need to separate them with regards to housing for taming. They are flock creatures and should take comfort from being together, unless they develop an antisocial issue. You may want to work with them separately, however. Good news is that as you work with one, the other will probably learn from watching the first.
Talking about the eye - see the eye of the bird on this page? The dark part is very small because the bird is excited. Making the pupil small like that is called pinning. It is not the normal relaxed look of the eye. What made you concerned that your birds are not young?