A cervical arterial dissection results in an intimal tear, which is intensely thrombogenic. Clot forms and propagates, and then can distally embolize resulting in a stroke. That stroke may respond to tPA. There are case reports of dissections treated with tPA in which additional strokes occurred presumably due to thrombus destabilization from the tPA. Damned either way, but the tPA is given to treat the embolic stroke, not the dissection itself.
Treating the dissection with antiplatelet or anticoagulant medications is done with the goal of stabilizing the thrombus adherent to the intimal tear to prevent distal embolization. One can debate the take-home message of CADISS, but antiplatelet management is likely equally effective in most cases to anticoagulation, at least at the population level, particularly in dissections that do not present with stroke.
Dissections can extend distally, and in rare cases can result in pseudoaneurysm formation which could in theory lead to rupture. This is very uncommon. The only time when we typically consider this is in the case of a V4 vert dissection (V4 is the intradural segment). Dissections often stop at the dura, but they can extend beyond it and the vessel has very little stromal support in the intradural segment. Therefore, minimal propogation of the dissection flap in V4 can cause subarachnoid hemorrhage. I have seen this, and it is indeed very bad.