What combo unit did you use?
Even in a combo, the rectifier and regulator are entirely separate components.
The rectifier is a set of power diodes that convert the 3-phase AC alternator output to a form of DC to charge the battery and power the bike's electrical parts.
The regulator controls the alternator output. It does this by powering the alternator field coil when the battery voltage is low, and not powering it when the battery voltage is high enough: it switches the field coil power on and off repeatedly several times a second when all is well and the battery is charged. The field coil takes quite a bit of power.
The rectifier is connected directly (no fuse) to the alternator stator coil wires, a good ground, and to the battery "+" terminal. The diodes will only allow power to go into the battery, not out from it.
The regulator does not know if the engine is running. With a stopped engine, the alternator can not make power and the battery voltage will drop if any load is connected. The regulator will then naturally turn on the field coil and since there's no power being made to raise the battery voltage, it will stay turned on (and drain your battery). The stock regulator has three terminals: BAT, GND, FIELD. The BAT is power in, used to both measure the voltage for deciding if the field should be turned on, and to power the field coil. GND is of course ground, needed to measure the battery voltage. FIELD is to the field coil.
Some combo units have a 4 wire regulator. They add a separate wire used for battery voltage measuring and for the field coil power: connecting this directly to battery "+" improves the accuracy of the measurement - this wire does not need to be switched. There's another wire that powers the regulator's electronics for measuring battery voltage and controlling the field power.
The regulator power must be switched with ignition, or the battery will be drained into the field coil as it tries to generate power from a non-turning alternator. This is the BAT terminal on the OEM regulator which connects to the ignition switch (black wires are switched ignition power in Honda bikes). For electronic regulators this is the control wire, not the battery wire: shutting off only the battery wire will cut off field coil power but you'll still be powering the regulator electronics - much less draw but still draining your battery when the ignition is off.
Electronic regulators use switching transistors to control the field coil. These can and do fail and become "leaky" - even though the electronic circuit is off the transistor can pass power to the field coil. If that's the case, when the control electronics power wire is disconnected, you will still have some power going to the field coil.
Aftermarket reg/rect units don't necessarily use the Honda wiring scheme so you have to look at the instructions to know which wire is which. Using a red wire for the direct battery connection to the rectifier is pretty standard though.
The least possible culprit is the rectifier. Since the stator coils are not grounded, even a bad rectifier can't drain the battery slowly back through the stator coil: they do sometimes fail (usually because of reversed polarity "jump-starting") and cause a high current "short" from bat "+" to ground but that will melt wires and smoke a lot, not just leave a dead battery overnight. It is very unlikely but still possible that a rectifier failure could drain the battery slowly.
If you don't have a meter you can check for power drain with a small 12V light bulb. With your ignition off, connect this bulb in between each of the reg/rect wire connections in turn with all the others connected. If the light lights - even dimly - the battery is being drained through that wire.
