Ranger One:
Transfer pump switches are there for that purpose - I've not flown the 135 myself, but on the AS 350, you use the transfer pumps when you want to transfer fuel from one tank to another - nothing more, nothing less. Fuel boost pumps (and not all machines have them) must be on all the time. I would not necessarily read anything sinister from the fact that the transfer pumps were off in this case.
Fuel low warning lights typically come on early enough so that you don't have to land immediately, but as with cars, the prudent pilot doesn't trust them! For example, you have around 6 minutes on some helicopters, but call it three. But you should certainly land in a suitable time frame.
Talking of which, you are supposed to have 30 minutes on a battery when the gennies stop working. I wonder if this one was up to speed when running the electrics which are required to fly a machine such as this.