GNOME Tweak is made for GNOME 3, not for MATE. They don’t manage the same things. To be more technical, the appearance settings are applied with what we call a daemon: the one that sets themes on GNOME (gnome-settings-daemon) is not the same as on MATE (mate-settings-daemon). GNOME Tweak will only work in GNOME (3).
Once you’ve installed a theme in /usr/share/themes (or ~/.themes), it should appear in the Appearance properties of MATE in the Control Center.
There are a few things to note, though:
- Themes made for GNOME 3 usually only include a Gtk3 version. They will work fine on Ubuntu MATE 18.04 but not 16.04. You’re on 18.04 so that’s ok.
- Themes made for GNOME 3 won’t always provide a Metacity theme, the appearance of the windows title bar, as GNOME now has its own way of handling title bars.
- Themes use and engine (a software that manages the way elements are drawn). If you don’t have the proper engine installed (from the repos or eventually manually), the themes won’t work.
- GNOME 3 also has its own format for the desktop panel and the ones from other DEs like MATE might not be styled as expected.
- There might be permissions issues when you manually install a theme (because the designers don’t always do things right), which can explain why it won’t apply.
So, to troubleshoot your issue, can you post a screenshot of your desktop after you’ve applied the theme (ideally with the themes properties opened −select the theme and click on "customize, then take a screenshot)?