Creating database with a relative path
The software installer is reading the %userprofile% or %homepath% environment variables to create the user database, you will have to change the installation script or temporary change the environment variables while running the installer. 

This has nothing to do with Express itself as it is creating the databases where it's asked to do so by the installation script. 
Now if you want to have the database in the home directory you are better off by using SQL Server Express LocalDB. I would consider this software a failure.