It is not entirely clear how your sequence was set up, for instance I am not sure if you are using sequence end times or target end times. If you can please include the sgf (sequence) file you were running and the logs we can take a look.
As a general rule, SGPro should never ask you any question that prevents end of sequence options from running. If it does need to present a dialog, it is typically self-expiring. The one exception to this is when the user asks for a sequence pause. In this case, the sequence will effectively end and perform no end of sequence actions… be careful with these. The only types of automatic pause are pre/post event and manual focus… neither of these seem to be what you are experiencing.
Since SGPro will never ask you if you want to keep imaging after an end time (in any way), and will just terminate the sequence (or target), I am not sure what you saw. Logs will probably help.