They also have us install software using the Fantastico De Luxe utility.
NOT a good idea and I would say your host is not familiar with Zen Cart. IF your host has the latest version from Fantastico AND IF that version of Fantastico has all the latest files, it MIGHT be okay to install a clean version of Zen Cart. It WILL automatically remove the installation files which might be needed for a database change. (Some folks install a clean 1.5.0 and then update their old database)
Fantastico WILL screw up an upgrade.