Every time is different when you go through it. For me the same situation happened twice with two different targets. The first being the archer guy in Jerusalem (I'll probably edit his name in later) and second the woman posing as Robert.
I start the sequence for each fighting off the guards but after chasing them (with them almost getting away) they run into Vigilantes leaving me to use my hidden blade.
Bad explanation but hilarious either way, has it ever happened to u?