Not sure if this is a bug or not, but everytime i install any application through GDebi (i.e Google Chrome and Lazarus IDE), it doesn't appear inmediately in the Applications Menu in their respective categories, notice this only happens in Traditional Layouts, other layout presets shows the icons perfectly without restarting or logout the system by changing them in MATE Tweak tool. i had this issue too in the previous LTS version of Ubuntu Mate.
Testing those packages again in different distros, like Linux Mint Xfce 19.3 and Kubuntu 20.04 their icons appear inmediately after GDebi (in Kubuntu case, QApt) finishes to install the packages.
Using MATE's own Menu Editor and Alacarte will show it as installed and checked-in for display as intended. My only workaround is using
nohup mate-panel --replace &
to force to reappear, it's a bit of annoying that happens in my favorite desktop layout.