Well you can set timeshift to backup your @home, but that is not a good idea for most people. If you use your home for storage of documents or music, videos the new stuff will be lost when you restore to an older date. Say you were working on a big project that you put a ton of effort into, all your work since your last snapshot would be lost.
That would upset many people, as well as potentially increasing the size of your snapshots by a vast amount (depending on what you store @home).
I actually do backup my home because I store very little there. My documents, music and videos are all stored on multiple external platter drives for an extra margin of safety.
Timeshift also has a setting to backup your dot (.) files in @home. This backs up your configuration files in your home directory and that is probably what you'd want to use with timeshift.
This of course is a double edged sword because if you messed a program configuration up and want it back as before that's great. However, say you had a bad update and your only choice was to roll back your system. Now you will lose all your configuration changes since your last snapshot.
The moral of the story is snapshots are not a replacement for a proper backup regimen. Most users never do proper backups until after they've experience a catastrophic data loss. Don't be "that" guy, get a proper backup strategy in place before you live to regret it.
I hope you don't mind too much, but I edited your title. It was not a "failure" on timeshift's part, it was an issue with your misunderstanding how the program actually works.