Actually there may be independent problems there :
1) First of all, make sure that 'psa-turba' RPM is installed:
rpm -q psa-turba
If it is not, you can install it with autoupdater or manually from the opt/horde/ directory in Plesk distributive tree.
2) Records in 'My AddressBook' are not shown.
It might happen if the 'horde.turba_objects' mysql table was not upgraded to Turba 2.0. In Turba v 2.0.3 horde developers wrote a uniformed sql script for upgrade instead of mysql-specific one. The problem is Linux specific and does not appear on FreeBSD and Debian.
In this case the 'horde.turba_objects' table should be updated manually with the following command:
# cat /usr/share/psa-horde/turba/scripts/upgrades/1.2_to_2.0.mysql.sql | mysql -uadmin -p`cat /etc/psa/.psa.shadow` horde
3) Records in 'Private' or additional AddressBooks are not shown.
To fix it, please, download the attached sources.php.gz file, gunzip it and replace the file
with the new copy.