Sorry but my view is that the purlin could be severely weakened. The traditional joint of choice would be a tusk tenon with a diminished haunch or to drop the plane of the principal rafter and run the purlin over the rafter. Nontraditional solution would be drop-in housing to receive square cut purlins with toe nails or log screws with simpson straps linking purlins across the rafter.
The tusk tenon and your spline method would require a more challenging assembly than a drop in or an over/under method.
I would also avoid the drop-in dovetail.
