You want to save the time when the button is pressed. This is neither tic/toc not cputime, but clock or now.
To accumulate the time stampes, you have to store them cummulatively, e.g.:
During the creation of the GUI:
handles.counter.push = ;
In the callback of the button:
handles = guidata(hObject);
handles.counter.push(end + 1) = now;
And finally in the function for saving, handles.counter.push contains all times the button was pressed.