You don't have to do anything - not if you transferred your iTunes library from your MacBook to the Mini and you have authorized the Mini with your iTunes account with iTunes and have iTunes Match enabled.
If you chose to have the backup for each device stored locally on your computer's hard drive when syncing each device with iTunes, iTunes will create and update the backup for each device as the first step during the iTunes sync process. You can also manually update the backup for each device with iTunes.
@ Big Al
OK, I clearly misunderstood you. I am a moron.
I have transferred my iTunes library to my Mac Mini
I have authorized my Mini with my iTunes account
I have iTunes Match enabled
But when I connected my iPod Touch (and then tried my iPhone 4S) to my Mini via USB nothing happened except it recognized them as "cameras" and opened iPhoto to download the photos on my camera roll. Nothing else happened. They didn't appear as "Devices" on the left column of the iTunes screen.
What am I missing/doing wrong?
With Big Al's help and some trial and error I have succeeded in transferring "ownership" of my 3 iDevices over to my new Mac Mini. However, as I expected, some "Poop Happened." However, it was not because of bad advice from the Big Boy.
Here is a summary for those attempting this in the future.
1. I THOUGHT I did a complete recreation of my MBP's iTunes library on my Mac Mini. Really. I did. I used Home Sharing between my MBP and my Mac Mini to import "everything" from the MBP's iTunes library to the Mac Mini. In almost every respect, that method worked beautifully. Highly recommended. What I had forgot is there was one glitch. It was with a collection of podcasts of Steve Jobs being interviewed by the folks from All Things Digital. I believe there are 6 video podcasts and one .pdf in the series. For some reason, there was a problem when I tried to import that particular podcast collection to my Mac Mini. So, I just bagged the import and went to the iTunes store and download the podcasts and .pdf, fresh and new, from the store. So, strictly speaking, my Mac Mini Library wasn't EXACTLY the same as my MBP's.
2. I then connected my iPod Touch 4G to my Mac MIni to start the process of coverting ownership of that iDevice to the Mini. Unfortunately, when I was done, there was a problem. It was that podcast series. When I went to set up wireless syncing of the iPod Touch I noticed that BOTH my MBP and my Mac Mini were listed under Wireless syncing! The MBP had podcasts under its name. The Mini had all other types of iTunes media under its name. I didn't even know this was possible. But, I knew this was not good. In fact, my iPod Touch would still try to connect with my MBP when I open iTunes on the MBP. It would also connect to my Mac Mini. This is not suppose to happen!
3. So, after some head scratching and messing around, with no luck at resolving the situation, I decided to restore the iPod Touch FROM BACKUP (while my iPod Touch was connected to my Mac Mini...of course). I first made a full backup of the iPod Touch to my computer then fired away and let the process run its course.
4. SUCCESS! The iPod Touch no longer had and remnants of its former life with the MBP. Under Wireless Syncing only the Mac Mini now appeared. I performed the procedure with my iPhone 4S and iPad 3 connected to my Mac Mini. Totally successful also. By that point it was 2:00 AM and time to go to bed.
5. I don't know if Big Al's advice would have worked if I had not messed with the podcast section of my iTunes library. But, I suspect it probably would have. So, my advice is...if you are going to do this, try at all costs to not change a thing when you recreate your iTunes library on your new machine. Even if it's just a new copy of the same media.
BTW, the restoring wasn't a total waste of time. I had accumulated about 7 GB of "other" data on my iPad. For those of you who are up on this issue, it can be a real problem as it robs your iDevice of its precious, limited memory. After restoring from backup the "other" data on my iPad had dropped to about 1 GB. I actually wasn't surprised that this happened as this is one of several workarounds folks have developed to deal with what appears to be a problem iOS 6 has with the management of "other" data.
Bring on iOS 7!
Oh! I forgot. One more piece of feedback. Big Al's link also helped me get my iDevices to appear under "Devices" in the left column of the iTunes screen. In my case, the suggestion from his link that worked was to shut down and restart my computer.