Unless a bit of speculation is correct and we're sent to repair a changed timeline where Grom was warned about the Legion, kicked both Ner'zhul and Gul'dan in the goolies and decided to form his own Horde, one that stood against the Legion when it arrived on Draenor.
Because this would inevitably spell doom for Azeroth, we're sent back to do... highly unethical stuff supposedly for the greater good. Make the orcs drink the demon blood. Make sure they invade Azeroth.
As for how it could start, it could be that the pre-expansion event features a Legion invasion that's at least partially successful, so Wrathion and his associates take matters into their own hands and bust Garrosh free (he does still hate the demons and all). I've speculated before that Kairoz made sure Garrosh survived the siege of Orgrimmar for whatever purpose (he and Wrathion could very well be allies). Perhaps when Garrosh is told that, he secretly finds a way to manipulate the Vision of Time and returns to the past where he warns Grom, explaining to him what would happen to their people if he listens to Ner'zhul.
We might be sent after him by a disgruntled Wrathion who feels his trust was betrayed and a great weapon taken from him. Another option is that both the timelines begin to merge together and it's not exactly in our best interests to keep it that way. In either case, we'd better take care of the mess if we want to return to our own time.