I dont see why it would be the achillies tendon as the tendon is not being stretched, unless its just alot of pressure on the tendon causing the pain.
Is the ankle that is sore being straightened? ( in the same way it would with a toe hold) if so you may get some tedon/ ligament stretching of the front of the ankle, try when doing the triangle to pull your toes back towards your knees as much as you can (dorsiflexion).
As for the person with the calf muscle feeling like its tearing once again the muscle is not being stretched or even activated while doing a triangle so im guesing its just being squashed from the pressure of your opponents back, try to adjust the angle that your leg goes over his head.
good luck