To sync both ways, and without using Internet storage clients like Drop box, I recommend using Chronosync. It's not the cheapest, but it's massively flexible. You set up a source and a destination, and provide configurable options for when and how to sync. You can sync both ways, sync but archive any files that are deleted, sync one way, sync when a machine logs into the same LAN, sync on a timed schedule, perform trial syncs to check what will change, filter against files within the sync area etc etc. I'm not affiliated with them in any way, but I use it to maintain 2 home directories on seperate Macs.
If you want to sync one way, you can use Folder Actions to make a copy for added files, but I don't think it will cater for file modification.
You say the folder is on your time machine drive, but you don't say how you connect to this drive (USB/Wireless etc) - you need to ensure that the drive that the folder is mountable on in available when performing a sync, whatever method you use.