It doesn't matter. Any even slightly competent driver would have NOT turned left at the point that the other driver had pulled along side of them. The obvious assumption is that the 2nd driver had not realized that the lead car was turning left (even though it had indicated that fact), but was instead turning right.
The alternative assumption is that the 2nd driver was acting aggressively and attempting to overtake on the turn.
For either of those conclusions, proceeding to turn left at that point, especially after only a short wait, is hazardous and almost certainly the wrong action to take.