I was wondering, does this particular choice has any effect on handling or aerodynamics?
Yes it does and it has to do with the fact that the two rotors are tilted sideward for obvious reasons of clearance between the two rotor heads.
Seen from above, the right rotor rotates clockwise and the left rotor counterclockwise but due to the sideward tilt, the rotors rotate also when seen from the side.
To simply picture it, just imagine them as being tilted sideward not just a few degrees but a full 90°: now they can be clearly seen rotating from the side. So, because of the sideward tilt, the rotors rotate both as seen from above and from the side.
In particular, from the side they rotate with the blade going up when leaving the tail and down when approaching the nose, as can be seen in the following picture¹ (yellow arrow):
As usual with helicopters, whenever a rotor rotates in one direction then the fuselage wants to rotate in the opposite direction (action-reaction law aka Newton's third law). In our case, since the two rotors rotate with the blades going down when approaching the nose then the fuselage wants to rotate nose-up (blue arrow):
(Obviously it would have been the other way around if the rotors had rotated in the opposite direction).
Now, somehow this blue nose-up tendency of the fuselage has to be opposed and the easiest way to do it is by tilting the rotors a bit forward in order to create a horizontal force (horizontal green arrow in the next picture) which generates a pitching-down moment in respect to the CG. Then, the thrust of the rotors not only lifts the helicopter (vertical green arrow) but produces also a pitching-down moment compensating the blue arrow:
Why are all those arrows good when pointing like that and not the other way around? Because this increases the longitudinal stability of the helicopter: let's suppose that the helicopter is invested by a vertical upgust. This upgust pushes the helicopter upward and increases the AoA of the rotors therefore increasing its thrust as well. In this condition a helicopter is stable if it reacts against these effects i.e. if it reacts pitching-down. And this is exactly what happen when all the arrows are how they are: the gust increases the thrust which increases the horizontal green arrow which increases its pitching-down moment opposing the gust and stabilising the helicopter longitudinally.
Another example² is a loss of power in hover: the stabilising effect results in a pitch down moment generating forward descent, which is a better starting point for an autorotation than a backwards nose up descent.
So, the rotors in an intermeshing design rotate as they rotate because this increases the longitudinal stability of the helicopter.
¹ all pictures from Wikipedia, modified by me.
² thanks to @qqjkztd.