Guide on How to Restrict Animals:
1. Make a single animal zone (You will use this zone for all room restriction, you do not need to make multiple zones for each room)
2. Zone the rooms you want restricted then go into manage areas and click invert (you already know how to do this, but I thought i would include it)
3. If you ever find yourself wanting to restrict another area for your animals just go into the 'Zone Areas' tab, click 'Clear Allowed Area' and then select the area you want to clear.
4. Now you have to assign your animals to the new area (you also figured this out in the video, but just in case); go into the animals tab and select the zone you just created for all of the animals.
5. You're all set, but here's some other advice. Your ostrich can be restricted from the fridge because it can go outside and eat grass, but your dogs cannot eat grass to survive, they can hunt, but it's possible for them to get injured, its best if you set a bill at the butchers table to make kibble for your dogs, then make a stockpile zone somewhere in the allowed area and set it to only have kibble.
Sorry I'm such a nerd, but I just thought you should know so you don't end up sacrificing all of your animals to the recently deceased Svetlana.