I can't really answer your question because there are several variables responsible for the dryer vent discharging into a ventilation shaft being code compliant or not. This "investigation" would most likely have go back to the building drawing mechanical blueprints.
There are several rules that may or may not apply to your condo and may or may not be enforced by your local jurisdiction. The best way would be to contact your local building department and describe this entire situation.
Although, dryer vent installations are permitted in some multi-unit / high-rise buildings (and jurisdictions), the ventilation system MUST be designed to properly handle it. Yours could require retro-fitting, and that's why your experiencing back-drafts from the dryer above.
Some of the requirements for the common ventilation shaft are:
material type (in most cases 26 gage or 30 gage sheet metal / smooth wall)
joint types (air tight / no screws shall penetrate walls to prevent lint accumulation)
proper fire rating of the shaft
adequate diameter to accommodate multiple appliances
access for lint cleaning (often top and bottom of the shaft)
booster motor on the roof (sometimes more than one) equipped with sensor detecting air pressure changes - usually they operate constantly on a low speed and accelerate whenever the dryer starts operating, dryer connections cannot be on the same level / across from each other, etc.
In case you'll get a negative response from the building department (claiming this installation illegal) you could suggest the association to require condo owners to use condensing type clothes dryers (they require condensate drain installation)
Let me know if you have any other questions.