I think the word immediate is incorrect in context because this has a specific meaning in the helicopter world like: Land NOW immediately. Further flight is not recommended. IE: MGB no oil, Double engine failure etc etc.. But I know where you are coming from.
Because there (normally) is a time gap between 1st and 2nd engine failure due to fuel starvation, there is time to set yourself up for a : LASAP.
Question: Was he flying over/about to fly over the river prior to landing at base or HAD he flown over the river prior to finals to the base?
Because if he had the river between himself and the base in sight and then the No1 stopped he would have been manouevring for a LASAP with the river as a potential obstacle. Now let's say the No2 stopped as he was commencing the crossing of the river (at a decent height because he only had one engine running), he may have thought he could have extended the flight path to clear the river by bleeding off some Nr...........never made it