backupmacostime-machineupgrade
I created a full backup from OS X 10.10.3 and I'd expect that sub-minor upgrade to be included in the backup. However this seems not true when I apply that backup in the initial setup-process of a mint MacBook—it will be a 10.10-version.
Is there a way to restore such a updates from a Time Machine backup? Respectively are the OS-files actually stored in the backup anyway?
It's possible. You should be able to click the Time Machine icon, then Open Time Machine Preferences... and then it will tell you a more detailed reason such as the following:
Time Machine works at a file level, with no facility to perform incremental changes within files. As such, your Sparsebundle may be backed up in it's entirety every time it changes in the slightest, depending on how large it is. Of course, you have to wait up to 1 hour (+the time it take to make the backup, depending on how large the queue is and where your file sits in it) to ensure those changes are included in the backup. Also if your Sparsebundle is in use (mounted...) then it may well skip it until the file lock is freed
This is a terrible system, and one that we might not see change until the underlying filesystem is suitable upgraded (or replaced) to include such useful facilities as incremental block level changes rather than simple file level ones, and/or deduplication etc. One early victim of this scenario were users who used the original Filevault system for encrypting their home folders. Time Machine would not backup their home folders until such time as they logged out because the Sparseimage file was constantly locked by the fact the user had it mounted. And even when the user did log out, it would proceed to make a hugely inefficient backup of the whole thing again and again - on the assumption that they simply logged out and didn't just turn off etc... Not very clever. To try to ameliorate this the Sparseimage spec was ammended to allow for Sparsebundles. Instead of a single big file, a sparse bundle is a bundle (directory) containing a number of files called bands, each in the order of 8 MB in size. This means even though to the end user the sparse bundle appears as a single file, it is composed of smaller files. As of Mac OS X 10.8, the bands are 8.4 MB each. When the content of the image changes, one or more band files is changed, created, or deleted. This allows backup software (such as Time Machine) to operate more efficiently, but it's just a bodge to attempt to mimic block level changes in individual files, which is limited to 8Mb "blocks"...
So to answer your questions directly, 1) it handles them properly, where properly means the same as any other file, it's just that your particular use (leaving it open and mounted) may not result in efficient backups that are taken regularly, especially if you rarely unmount the file, and 2) yes, you will need to pull back the whole file to view it's contents. The TM restore interface is also file specific. It may have quick-look plugins to allow you to view simple files inline like JPGs etc, but not for a complex file like a sparsebundle.
On the bright side, you already have a licensed copy of ChronoSync, which is super useful, and I would continue to use this to perform incremental backups of your sparsebundle whilst it is mounted, you can use the same drive as your TM images too.
Best Answer
Unless you excluded the OS files from the backup, Time Machine should've backed that up along with everything else; but in order to recover the entire OS (rather than just your user files), you have to do the restore differently: use the restore tool in Recovery Mode (reachable by starting the Mac with Command and R held down). However, there are a couple of warnings I should give about this route:
Because of the above, I'd be inclined to stick with the restore you have, and simply reinstall the update.
BTW, the question seems to contain a bit of a misunderstanding about how OS updates and backups work. Time Machine (and other backup systems) back up files and folders. An OS update isn't a file or folder that can be backed up as an item; instead, it's a bunch of changes to various system files and folders. If those files and folders are being backed up, the updated versions will be backed up; if not, they won't be. Similarly, you can't restore a system update, you can only restore the changed versions of the various system files (and since you don't know precisely which ones were changed, that pretty much means restoring all of the system files and folders).