Should I get all drivers from third-party websites or Windows to do it?
Windows performs a routine maintenance check every so many hours. One of the tasks it does is checking if there is a problem with hardware. It will try to fix it automatically or, if not capable, inform the user.
One of the methods of fixing a driver issue, is by checking if a new driver is available online. If so, it will download the driver and install it.
The driverpool Windows uses may or may not be the latest driver available, but it will be a stable driver, unless it somehow is incompatible (usually happens just after a major Windows update). The driver may be a slimmed down version though, but most of the time, that is enough.
In any case, it is safe to use these drivers.
Updating to those provided by the web, can be beneficial, but it may also install a different version of the exact same drivers already installed (for example, Microsoft installed an English driver, and you downloaded the one native to your language).
The only time when using the drivers from the manufacturer website is important, is when you talk about graphics drivers, especially those by AMD and Nvidia, as they continuously tweak their drivers to give better performance.
Microsoft usually does not update the drivers in their driverpool that frequently. If you use hardware that is older, the drivers provided by Microsoft will likely be the latest.
So: Should you update every single device with new drivers from the manufacturer website? My advise is: only if you are missing features or noticing performance issues. When I format my Windows, I rarely install other drivers. Only for my video card and sound card, as they both require special drivers to access the hardware exclusively.
Several questions are being asked here, I'll try to answer them all in proper order.
Should I get all drivers from third party websites or allows windows to do it?
You should look yourself for drivers on the manufacturers' websites. This way, you are guaranteed to get the most updated drivers for your devices. Allowing Windows Update to install drivers is a risk, and I would not recommend it unless the peripheral did not work and there were no other options available. It has happened (to me, to people I know, to users of this website) that Windows Update installed a driver and the system became unbootable or unstable.
I see the drivers updated. Is this correct behavior?
Yes. Windows itself includes some drivers that do not have to be downloaded from Windows Update. Take as an example the drivers that get installed automatically whenever you insert a USB storage stick.
Do I need to visit the 3rd party web sites to download drivers or is this not necessary as I do not see any issues in the device manager?
It is not necessary, but desirable: it warrants you get the latest drivers and all available fixes and performance improvements. Third-party website should mean the pc or perpheral manufacturer's website, and not just any website offering drivers for download.