How about the old ARA rule of thumb “Don’t overfly at less than 1500’ any radar target you have not positively identified.”
we used 1000' in the UKSAR force but if you haven't seen the contact, you can't apply that rule.
The problem wasn't only that they didn't detect the threat until very late but that the reaction was so slow - it was done like a routine turn at a WP - the PF acknowledges that a turn is required, then asks the PNF to adjust the heading bug, then the heading bug gets moved and finally the aircraft starts to turn.
Use the automation by all means but be prepared to take immediate action when it is - as it was in this case - required.