It's aftermarket but do think it decreased the voltage.
I'm starting to think the stator is putting out too much voltage, and that burned out the original rectifier and increased the idle.
Probably need to check the voltage of the stator output; and find some videos online to do it.
Would the CCI have any effect on these readings?
As far as I know a stator simply can not put out higher than normal voltage.
Maybe you should also check if the voltage keep on kreeping up quite fast just after the engine has been started. If so, that can be an indication of a faulty or incorrect voltage regulator.
Like somebody mentioned here — maybe only an OEM regulator should be used.
The 13+ voltage reading you got when the engine was not running could be normal - but only if you got the reading just after the engine was running, or just after the battery has been charged with a charger. The Voltage should drop to less than 13 volts after the battery was just standing for a while.