Buttons switches in Delphi
It seems I found better solution. All these buttons are located on ToolBar.

I can loop through the ToolBar and utilize the Name property on the buttons to compare with. So, I've changed it to:

  var
    LSelectionType, i: Integer;
    LButtonName: string;
  begin
    LSelectionType := 1;
    LButtonName := (Sender as TAction).ActionComponent.Name;    
    for i := 0 to ToolBar.ButtonCount -1 do
    begin
      ToolBar.Buttons[i].Down := (ToolBar.Buttons[i].Name = LButtonName);
      if ToolBar.Buttons[i].Down then
        LSelectionType := i + 1;
    end;
    ...
  end;


UPDATE

Finally, I set proper Tag property and set property Grouped to True for buttons and changed code:

  var
    LSelectionType: Integer;
    LActionComponent: TComponent;
  begin
    LSelectionType := 1;
    LActionComponent := (Sender as TAction).ActionComponent;

    if LActionComponent is TToolButton then
    begin
      (LActionComponent as TToolButton).Down := True;
      LSelectionType := (LActionComponent as TToolButton).Tag;
    end;
    // and using LSelectionType 
    ....
  end;