Enable auto download: Setup > Game options > Automatic Downloading : on.
Alternatively check your q3config.cfg for cl_allowDownload and set it to:1
OR type in-game: /cl_autodownload 1 in the console (SHIFT+ESC).
This is most likely due to the freaking config file location. Every Quake3 MOD has its own q3config.cfg! If you start the game, you're starting baseq3. When you later join an Excessive server, Quake might load the q3config.cfg in your old excessiveplus mod-directory. This might contain wrong / old settings.
Probably the best approach is to delete the q3config.cfg from every mod-directory but baseq3. Then do all your settings - either in-game or in your baseq3 config (cl_allowdownload, bind q +button5 ect.) This way Quake3 will copy your baseq3 q3config.cfg over to new mods.
NOTE: the config location is not the game location! That would have been to easy. It's here:
Windows: %APPDATA%\Quake3
macOS: ~/Library/Application Support/Quake3
Linux: ~/.q3a
Whatever dark soul possesses your PC, just download the map-pack and extract it to your baseq3 directory.