There are at least three different alternator "C" terminal systems that I am aware of.
With the oldest one, it was power out from the star point of the stator for such as an electric choke.
Ones connected to the PCM include:
A simply full output / limited output control, using high / low voltage (around 8 - 9V and near 0V).
PWM control using a fairly low frequency signal. With that, the duty cycle controls the regulator output voltage setting, as long as it's a valid PWM signal, never continuously off or on.
A disconnection or fixed level switches the alternator back to internal regulation at normal battery full voltage, ~14.5V
There are likely others as well.
In general, the C pin is used to reduce alternator output (and engine load) during acceleration, and possibly increase it during engine braking, with PWM controlled types. PWM is also used with AGM batteries to improve charge control on start/stop systems.
The alternator itself should usually default to conventional operation with C disconnected; no PWM or an internal pullup setting it in full output mode.
It's always possible the replacement is faulty!
What's the exact vehicle make, model and year?