Tenant complaining about mildew by AC Vents

[Victor Texas]

I'm new here so please bear with me as I ask my first question in this forum. I have a tenant who has been in the property for the past 3 years. They just highlighted a problem of mildew growing by the AC vents. I recommended that they reduce the amount of moisture in their home, since I visited them and saw that they keep the home fully closed and dark, could sense the moisture in the home. Any other recommendation from the experts here. I'm not sure if I should get an HVAC professional to go check the HVAC, which is about 9 years old but has been working fine with no issues, or tell the tenant to clean this with a rag and clorox to keep it under control. 

I also checked the vents and they were professionally cleaned 2 years ago and are still clean. Would appreciate any thoughts or guidance. Thanks.

Victor