At the present time, the SmartThings hub does not have the ability to do “over the air” firmware updates (OTA). They have said they would like to add that in the future for both Z wave plus and zigbee, but they don’t have it now.
So for now, the only way to do updates for many of these kinds of devices is to have another controller which is capable of doing OTA updates, move the device over to that controller, do the update, and then move it back to SmartThings.
If that all sounds like a lot of work, it is. 
The only community members I know who do this on a regular basis are some of those with Osram Lightify bulbs who also purchased the lightify Gateway as part of a package deal. If Osram does a big update, they sometimes move the bulbs back to the Osram Gatewayto get that done.
Some manufacturers, such as Aeon labs, do publish firmware updates as downloads on their site, and you can download the file to a laptop and use a USB cable to Connect those devices (like the Aeotec minimote) to do the update that way. Obviously that doesn’t apply to bulbs and other devices that don’t have USB connectivity.
And as you mentioned, some manufacturers have their own Internet connectivity, such as the Phillips hue bridge, the Logitech Harmony hub, ecobee, and others, and those will just handle their own updates in the usual way.
But for now, SmartThings does not provide OTA firmware updates for Z wave or zigbee devices connected directly to the SmartThings hub.
The following thread has some staff discussion: