Had a look through the instructions and nothing to suggest you should need headlights on (or DRL's) for turn signals to function. However the standard turn signal setup is controlled by a "TSM and headlamp" module which has been known to cause vagueries (used to very occasionally get uncommanded hazard function, cured by turning hazard switch on then off). Given this, might be worth hooking up the ground side of turn signals (white wire) to ground (black) on JWS headlamps. Note the instruction sheet shows two plug and play connectors for headlamp and turn signal with the latter connecting to both OE turning signal cables.
Other US M3W owners have fitted JWS headlamps but maybe EVO 2's although I remember one TM member fitting a version with integrated turn signals. In any case suggest you contact JWS. Are you keeping OE turn signal lamps and adding the JWS ones in parallel BTW? It shouldn't make any difference given low current draw but who knows.
Other observations: There is mention of a lens heater (30 watt) on the back of lamp.
Assuming your headlamp switch has a redundant sidelight position (I know latest versions are simple on/off), you could add position lights by extending the red/orange and red/black wires each side that have been cut off inside your headlamp buckets, or you could hook them up to DRL connection depending on what is legal in your state.
