I'm not sure about what really is the rule. Like I understood it originally, dual-way switching required:
1 - Getting to the bifurcation
2 - Actually picking one of the two ways and entering at least one tile of one of them
3 - Leaving the path at some point before the two ways join again
4 - Entering the other path at some intermediate point too
5 - Reaching the union again
But here, this is not the case, as you never actually join one of the two paths. Now, I could think it's enough with just leaving the path and then rejoining the same path, but is it required that the same path be re-entered from a tile other than the one it was left to? I am not watching the RPL right now, but let me see if I remember correctly:
1 - You first reached the split, then took the purple path
2 - You drove the two closed corners, leaving the second tile (second corner) toward the east
3 - You drove south to the tile containing the palm tree
4 - You re-entered the same path from the north into the last purple tile (fourth corner)
5 - You got to the crossing and turned west
Is this correct?