Your camera can only meter the light in the scene. The flash hasn't flashed yet, so there's no flash for the camera's meter to measure and account for.
Your camera can adjust the built-in flash automatically because it can "speak" to the flash to perform TTL (through the lens) metering. The camera tells the flash to fire a "preburst" of light at a known brightness/power level, meters the preburst, and based on the reading it gets, can adjust the power level of the flash to where it thinks a good exposure level is.
The key here is how the camera speaks to the flash. On the flash hotshoe, there are a number of contacts for the pins on the flash's foot. The one in the center of the square is the "fire" signal. The other four pins below that are how the camera communicates the preflash firing signal, different types of sync timing, and power level cutoffs, as well as adjusting settings on the flash. The Neewer TT560 only has the center sync pin on its foot. So it can't communicate anything but to fire in sync: no 2nd curtain, no TTL, no HSS, no remote control from the camera's menu. So, it can't do the TTL metering thing in concert with your camera. For that you'd need a TTL-capable flash that has all five pins on the foot.
To properly expose with this flash, you have to manually set the power level yourself on the flash's back. You can always adjust and chimp (i.e., see what you got, adjust and reshoot until you're where you want to be), do mental calculations with your flash's guide number (I.e., the guide number, divided by your aperture setting's f-number is the distance that's appropriate for your flash at a given ISO), or use an external flash meter that can measure the light from your flash and tell you what aperture setting you should use for a given ISO.
Alternatively, there are now some relatively low-cost TTL 3rd-party flashes, from makers like Neewer and Yongnuo. They're not as cheap as the manual-only models, but they're 1/2 to 1/3 the price of the OEM flashes. Just don't expect the same reliability, component quality, copy consistency, warranty service, or resale values as with the OEM units.