Lost it all

I bought a 1tb usb 3.0 drive for time machine backups. Backed up my MBA, my wife's Mac Mini and my Mac Mini.
I lost the ability to connect to wifi on my Mac Mini and after trying to fix the problem without success, I figured well just do a restore.
I did.
The restore somehow took my wifes setup and put it on my machine. When I looked on the 1tb drive I saw that my backup was listed but it wasn't used.
Don't believe them when they say that Yosemite can use the same hard drive for all your machines and time machine will keep things separate. Luckily, its a pretty new machine and I did save all created info to a thumb drive. But what a pain.
I'm putting a fresh copy of Yosemite on now.. only 2 hours and 48 minutes to go.

Sigh. I guess the new factor was my biggest problem. The machine is new... the time machine backup is recent, the drive to store the backup is new and the knowledge is limited. lol
But I'm learning. The up side is that there wasn't much to lose since I saved all of my created files to a thumb drive before trying to fix the wifi issue.
I will take all of your advice and put it to good use.
I downloaded another fresh copy of Yosemite, and to my surprise it came up to my wife's setup again with no back up drives attached, because I had not thoroughly cleaned the machine before reinstalling. So, I added myself as an admin and deleted her account from my machine. I went into Sharing and renamed the machine to my original computer name . Anyway, I'm up and running again as me. Lesson learned.
Thanks everyone for the advice.