Time Machine doesn't have to have a recovery partition. I think that option was added in time machine 2.0, and gets installed/updated when you upgrade your os. (I don't believe it updates it when you run an os update, like from 10.9.3 to 10.9.4)
In my case, I migrated a 10.6 system from a Mac Pro to an iMac with 10.10 pre-installed. Thanks for the clarification. I'll look into it.
OS 10.14.6, iMac Retina 5K 27-inch, late 2014, 3.5 GHz Intel Core i5, 1 TB fusion drive, 16 GB RAM, Epson SureColor P600, Photoshop CC, Lightroom CC, MS Office 365