No one can tell you what is happening without inspecting the property. Is there are reason you doubt the professional? Seek a second opinion if so, a professional opinion not reddit.

The mold is a concern, but the white fluffy stuff is mostly allergy issues that develop over time. If no one has respiratory symptoms it's not any acute threat.

But in general, moisture/vapor problems are quite serious and absolutely need to be addressed. It's worth taking the effort to really identify the issue and fix them properly. It might take a lot of effort finding an appropriate inspector and contractor.