Are they allowed to do this without issuing a citation or warning first?

IANAL but the way the towing provisions of the civil code are written are kind of weird. The way it reads seems to indicate that if they have signs up that the property is private and vehicles can be towed from it (with tow co. info on the sign), then they can do so if you violate their rules. However I believe the intent of the civil code was that they are supposed to either post the rules at every entrance, or give the vehicle a 96-hour notice of the violation before towing. However if you are double-parked in front of a driveway, they could make the argument you are "blocking access" which is grounds for immediate removal anyway.

The big question is whether the HOA rules even apply in this situation. I am not clear on the definition of your property. You say it is "private property" but it's unclear if your vehicle was parked on a private property that is not part of the association, on a separate interest within the association, in the association's common area, or in your exclusive use common area for your property. This could greatly change enforceability depending on which applies.

-HOA manager