Ubuntu desktop (based on Gnome Shell) uses a "Launch or Switch" paradigm. If you click a launcher in the dock, the program is started if it is not yet running. If the program is running already, you will switch to it, even if it is on another workspace.
Still, you can deliberately choose to launch a new instance instead of switching to an already running instance: hit the Ctrl key while clicking the launcher, or middle-click the launcher.
Yet, it is easy to change the behaviour to what you want
Open the terminal, and execute following command to change a Dock setting.
gsettings set org.gnome.shell.extensions.dash-to-dock isolate-workspaces true
Now, the system will behave like you prefer. The Dock will only show icons for programs running on the current workspace. It also will always show all your pinned applications, ready to be launched. Now also your Browser will launch on the new workspace, even if it is already running on another workspace.
To undo this setting, just reset the setting to its default:
gsettings reset org.gnome.shell.extensions.dash-to-dock isolate-workspaces