To trigger the Awakened Dragon passive from Spear of Shojin you have to auto something within 10 seconds of using her ult. The first cast of her ult does proc Spear but does not grant awakened dragon until you auto so after the 10 seconds it will go on a 30 second cooldown which generally makes Spear terrible on Quinn.
Recalling puts Quinn into her ult but will not activate spear, so in this case the second part of her ult will activate the 10 second window to try and auto the enemy for awakened dragon. The other option is while in lane, just go into a bush or back behind your turret, go into ult, fly up in lane second cast ult within a couple of seconds, then auto and you will get the full use of awakened dragon still.
In general though I would not recommend this item for Quinn, there are higher value items for her and if you try to use it to roam, since the window starts after first ult cast it will almost always time out before you get there and just do nothing as a passive. It can be used to be pretty obnoxious in lane though.