This is happening on every site whether it be pre Joomla 3.4.4 to the current 3.4.4. The only way we found to get the install to work is via the Joomla extension manager and with over 200 Joomla sites, this update will be a royal PITA to install on all sites by hand.
It seems that module parameters haven't been configured properly. Please make sure that you are using a valid twitter username, and
that you have inserted the correct keys. Detailed instructions are written in the module settings page.