If you migrated from the Evolution PIM to Thunderbird, you will find that the contacts list in Thunderbird is not able to display all the address book elements that were entered in the Evolution PIM address book.
Also, Thunderbird cannot synchronize contacts with the mobile phones. To overcome this issue, do not kill the Contacts in the Evolution PIM. Leave them as it is.
To use them in Thunderbird, you need to install a Thunderbird Add-On called EDS Contacts Integration. Here is the now active project. Enable it and restart Thunderbird. Now, when you type the email address in Thunderbird, you will find that it fetches them from Evolution.
You will need to manage your address book using Evolution and not Thunderbird.
Right now, the EDS Contact Integration add-on is not available at the Mozilla Add-ons site for Thunderbird. However, it is under extensive development at launchpad.