No, Time Machine is not truly a disk image. There is a disk image within Time Machine that is created and has data from the first backup. Thereafter, only new, never backed up files are added to the disk image (more precisely, it is called a sparse bundle.) Existing files that have been changed since their original backup are not entirely backed up. Rather, Time Machine only backs up the changes to save space on the backup drive. Every hour Time Machine performs an interim backup in order to catch as many file changes. Time Machine does backup system files, so it is possible to restore an existing startup volume such that it is bootable.
Because you already erased the drive and reinstalled OS X, there is no need to fully restore the whole Time Machine backup. What you want to do is restore your data which are contained in the Home folder. This can be done using the Setup Assistant during the OS installation or using Migration Assistant after the OS has already been installed. This latter is what you will need to do since OS X has been installed. The links below are various articles on the use of Migration Assistant to restore your data. MA can transfer your Home folder but will not overwrite an existing Home folder. If you have configured a Home folder during OS X installation, then you will end up with two Home folders. You will need to restart the computer and at the login screen, choose your migrated account for login. Then you can delete the account you setup during OS installation.
How to move your content to a new Mac
How to use Migration Assistant to transfer files from another Mac
Setting up a new (or repurposed) Mac- 2 Migration Assistant
How to Use Migration Assistant with macOS Catalina
Setting up a new (or repurposed) Mac- 3 Manual migration
