Q: Time machine backup to older OS?

Depends on what is the minimum version of OS X the newer iMac requires. If it came with 10.7.x installed when it was new, then you cannot run a lesser version of OS X.

Just s different method that requires either a Snow Leopard installer DVD or one that came with the computer when new.

Clean Install of Snow Leopard

Be sure you have backed up your files because the following procedure will remove everything from the hard drive.

     1. Boot the computer using the Snow Leopard Installer Disc or the Disc 1 that came

         with your computer.  Insert the disc into the optical drive and restart the computer.

         After the chime press and hold down the  "C" key.  Release the key when you see

         a small spinning gear appear below the dark gray Apple logo.

     2. After the installer loads select your language and click on the Continue

         button. When the menu bar appears select Disk Utility from the Utilities menu.

         After DU loads select the hard drive entry from the left side list (mfgr.'s ID and drive

         size.)  Click on the Partition tab in the DU main window.  Set the number of

         partitions to one (1) from the Partitions drop down menu, click on Options button

         and select GUID, click on OK, then set the format type to MacOS Extended

         (Journaled, if supported), then click on the Apply button.

     3. When the formatting has completed quit DU and return to the installer.  Proceed

         with the OS X installation and follow the directions included with the installer.

     4. When the installation has completed your computer will Restart into the Setup

         Assistant. After you finish Setup Assistant will complete the installation after which

         you will be running a fresh install of OS X.  You can now begin the update process

         by opening Software Update and installing all recommended updates to bring your

         installation current.

     5. If you are planning to sell or give your computer away, then do the following:

        After you reformat your hard drive and reinstall OS X, the computer restarts to a

        Welcome screen and asks you to choose a country or region. If you want to leave

        the Mac in an out-of-box state, don't continue with the setup of your system. Instead,

        press Command-Q to shut down the Mac. When the new owner turns on the Mac,

        the Setup Assistant will guide them through the setup process.

Download and install Mac OS X 10.6.8 Update Combo v1.1.

If they cannot run Snow Leopard, then you will need to have the original installer discs that came with them when they were first purchased.

All you should have on the  HDD when you dispose of the computer is the OS that was originally installed or Snow Leopard.

Upgrading to Snow Leopard

 

You can purchase Snow Leopard through the Apple Store: Mac OS X 10.6 Snow Leopard - Apple Store (U.S.). The price is $19.99 plus tax. You will be sent physical media by mail after placing your order.

 

After you install Snow Leopard you will have to download and install the Mac OS X 10.6.8 Update Combo v1.1 to update Snow Leopard to 10.6.8 and give you access to the App Store. Access to the App Store enables you to download Mavericks if your computer meets the requirements.

 

     Snow Leopard General Requirements

 

       1. Mac computer with an Intel processor

       2. 1GB of memory

       3. 5GB of available disk space

       4. DVD drive for installation

       5. Some features require a compatible Internet service provider;

           fees may apply.

       6. Some features require Apple’s iCloud services; fees and

           terms apply.

Do not install any of your software. Erase the drive and install the original software that came with it when new or the retail version of Snow Leopard.

Before Selling or Giving Away Your Pre-Lion Mac

Follow these instructions until you get to Step 5:

          What to do before selling or giving away your Mac - Apple Support

When you reach Step 5 you will need your Snow Leopard or earlier installer disc that came with the computer when it was new.

1. Follow these steps for installing the original version of OS  that came with the computer.

     1. Boot the computer using the Snow Leopard Installer Disc or the Disc 1 that came

         with your computer.  Insert the disc into the optical drive and restart the computer.

         After the chime press and hold down the  "C" key.  Release the key when you see

         a small spinning gear appear below the dark gray Apple logo.

     2. After the installer loads select your language and click on the Continue

         button. When the menu bar appears select Disk Utility from the Utilities menu.

         After Disk Utility loads select the hard drive entry from the left side list (mfgr.'s ID and

         drive size.)  Click on the Partition tab in the DU main window.  Set the number of

         partitions to one (1) from the Partitions drop down menu, click on Options button

         and select GUID, click on OK, then set the format type to MacOS Extended

         (Journaled), then click on the Apply button.

     3. When the formatting has completed quit DU and return to the installer.  Proceed

         with the OS X installation and follow the directions included with the installer.

     4. If you are planning to sell or give your computer away, then do the following:

        After you reformat your hard drive and reinstall OS X, the computer restarts to a

        Welcome screen and asks you to choose a country or region. If you want to leave

        the Mac in an out-of-box state, don't continue with the setup of your system. Instead,

        press Command-Q to shut down the Mac. When the new owner turns on the Mac,

        the Setup Assistant will guide them through the setup process.