No, you shouldn’t. The updates should propagate in some rolling manner, so all one has to do is wait.
If you think your camera or sync module is really missing a firmware update, power cycling the device could make it check for a new one as it restarts, but probably no guarantee.
As @ronsec said, support can also push a firmware update if it’s warranted.
The more recent versions of the Blink app have added the ability to see camera firmware versions, not just sync modules. Which is a welcome addition.