Fax machine and digital voice service problem

I recently switched to triple play. When the tech came out to do the installation, I asked him about if I can add a fax machine if I decide to later. He said "absolutely". He told me to just add a splitter right in the back of the modem and plug in both my fax machine and the line for phone signal.
Now that I'm ready to add a fax machine, it doesn't work! As soon as I plug the fax machine in, the phone service stops working. It sounds as if the fax machine took the phone off the hook. even though the Auto Answer is set to off! It's a disaster and now I've spent money on a new All-in-One printer and can't use the fax!