The pads are intumescent - they expand to form a fire seal in the event of a fire but do not stop smoke which is generated in the initial phases of a fire at lower temperatures. Cold smoke seals ("brush strips") are designed to limit the movement of smoke from the room in which it is being generated so losing a small amount of sealing for the hinges and lock plate is generally regarded as acceptable. You can get specific three side sealed door sets but the are rarely specified as they must come a a complete door/frame set. Remember that there will in any case be a 6 to 10mm gap at the bottom of the door....
What you probably need are called combined smoke seal and intumescent strips. These normally come in 15 and 20mm widths and are most easily routed using an intumescent strip cutter - you will need to take the door down and rest it on trestles as well as remove any ironmongery which will get it the way of the router cutter or baseplate (e.g. hinges, lock, finger plates, kick plates, door handles, etc)