Matlab installs without a glitch. However, there is no integration with Budgie. No .desktop files are created and I cannot find any icon files in /usr/share/icons. Not sure what's going on.
Debian based distros have a separate script which users run after installing Matlab, which takes care of these things. Have found this. The problem is, Matlab installation in Solus does not create a /usr/share/app-install/ directory at all.
Note: This does not affect immediate functionality as Matlab can be launched via the terminal. But it would keep a lot of scientists from trying Solus as Matlab is the most commonly used computational tool.