Ok first of it's called a shutter button not capture button. Secondly you should know that all cameras function pretty much 95% the same with the same terminology. All Digital cameras are built with the same settings and functionality of older analogue cameras, to keep it familiar with pro photographers. If Canon for example, redesigned the digital camera with new features and terminology, nobody would buy it. The only difference betweeen a $300 camera body, and a $5000 body is the number of features that are adjustable as opposed to fixed and automatic, beside the quality of focusing, etc... So good news is, even a $300 camera can take amazing pictures. It's the lens that determines quality. Also you can learn photography with your A5000, and in the future if you move to a different brand such as Nikon or Canon it will be familiar. Once you learn the photography jargon all cameras are basically the same in usage.
As for your question. Whether a lens can maintain focus while zooming is a function of the lens not the camera. More expensive lenses can, and some cheaper lenses can't track as well. A test is to zoom all the way, focus, then zoom out. If it maintains focus it tracks well. If you start zoomed out, focus, then zoom it it'll have a harder time to track focus properly. Even with expensive lenses.
Now you said you focus, zoom in, and then it snaps a picture of the zoomed out image. This is almost impossible. It can only take a picture of where the lens is in time. When snapping a picture it won't unzoom the lens then take the picture. So I don't understand. Also zooming while focused is only used in 2 situations.
1 is for taking movies. An SLR camera can shoot amazing movies with a 15-50mm or so lens and if its a good one you can zoom in and out and it'll track the focusing while doing so.
Situation 2 is if you are in continuous mode to snap 7 pictures/second or so depending on camera specs. More expensive cameras can do more pics per second. This is for taking pictures of a moving subject such as a cheetah on the run or a bird in flight. You can zoom in out while snapping pics continuously to try and capture that perfect shot. When done filter through the 100 pictures you just took and keep the magic one, deleting the rest.
Otherwise you must zoom to frame your picture the way you want, then focus and take the picture. No need to zoom while focusing. And if you still can't focus properly you need to manually focus with the ring or adjust your focus settings. Some lenses just don't auto focus properly. But in no way is it possible for a camera to take a zoomed out pic while zoomed in. Unless you pre snapped the pic by accident then started zooming in and got confused.