The reason lies in the instability of helicopters.
Contrary to airplanes, helicopters aren't naturally stable. One hand is constantly on the cyclic stick (the main control) to adjust the aircraft attitude. For a right-handed pilot, the delicate and uninterrupted task of maintaining stability is more easily carried out using the right-hand. This implies the left hand has the burden to manipulate all other controls.
With helicopters controllable from a single seat, this was not a problem, the second control in order of importance, the collective lever, was located on the left side of the pilot. This allowed to use the airplane configuration with the pilot on the left side.
The problem appeared with dual-controlled helicopters which were also more complex aircraft: There were many controls between the two seats, so they can be used by both pilots. After a quick experimentation, it was clear the left-hand should be close to these controls.
The main pilot seat was therefore shifted to the right one, and a single collective lever was positioned, with other existing controls, between the seats.
At the beginning: No difference with airplane
First dual seats helicopters were piloted from the left seat, exactly like other aircraft. Focke-Achgelis FA 223:
Pilot used their left hand for the power lever (collective) and the cyclic stick was under right hand control. Bell HTL-4:
Return of experience: Handle cyclic with left hand
Contrary to an airplane, there is no stability on an helicopter, even less at that time. The rotor had to be adjusted continuously to maintain a safe attitude. On the other side, the collective with its rotating ring could be kept in a given position without hand contact.
Pilot right hand being unavailable for something else than the stick, radio buttons manipulation, tank selection and other tasks had to be conducted with the left hand.
However it appeared quickly this was not the best configuration for a single pilot, the left hand having a more limited reach than the right one in the middle of the cockpit.
Dual seat aircraft means also a possibility for dual controls and two pilots, some controls have to be located on a central console, more difficult to reach with the left hand.
Designers were quick to move the collective lever in the middle, meaning a pilot used to control the collective with the left hand would seat in the right seat to continue piloting the same way. One of the first helicopter to use this configuration has been the Sikorsky H-19 (HRS-3).
Sikorsky H-19 (Youtube)
It's visible on the previous image, from an ergonomics standpoint, this configuration allows for the free hand (left) to reach a lot of levers and switches while the other is constantly busy adjusting the cyclic stick to keep the helicopter in a safe attitude.
For left-handed people, the "weak" hand will have to do the latter task, this will be a little less easy. For them, the initial "airplane" configuration was clearly an advantage. With dual-control helicopters, left-handed pilots could sit in the left seat if they preferred, but as for airplanes, the standard (right-handed) arrangement is used.
An additional detail: "Why is the PIC position for helicopters the right seat" -- PIC (pilot in command) is not synonymous to PF (pilot flying). The above details pertain to PF. PIC could seat anywhere as long as they are not flying the aircraft.