Lulo,
Thanks for the post. iTunes is supposed to handle the backup of 3rd party app data. However, as many have noted, this doesn't always happen the way it's supposed to. The good news: we're adding a built-in backup/restore function to the next version of timewerks (1.7, due in about a month). The bad news: this doesn't help you in your current situation. We have found that the following works, but it assumes you have a recent backup of your previous device:
To copy Timewerks data from your old phone to a new phone, you must first make sure your current phone is backed up in iTunes.
Basically:
1) Connect your existing phone to iTunes
2) Right click and select backup.
3) When you connect your new phone, it will ask if you want to set it up from a backup of an existing device.
4) Choose yes and select the backup you made in step 2.
Here's more info on iTunes backups direct from Apple:
http://support.apple.com/kb/HT1766