For some reason I cannot understand fully there is a problem with the key <Ctrl> in Terminator. If you configure <Ctrl>+t, for example, for creating new tabs the configuration doesn't works and is not saved. The problem is described here. The temporal solution of the problem consist in editing the Terminator configuration file in:
bash$ vim ~/.config/terminator/config
And change by hand the key binding for creating new tabs to
... tab_position = hidden [keybindings] new_tab =t next_tab = Right ...
The problem seems related to Terminator using the key <Primary> instead of <Ctrl>.