So I want to install a drop ceiling in my basement, but I have these TJI/ I-beam type engineered wood floor joists and I know that you should almost never nail or screw into them on their bottom flange. So, How does someone install a suspended ceiling with these type of joists then?
Suspended ceilings are lightweight enough that you can attach to the bottom rails. Just don't use fasteners so large that they're splitting things, and come in from below or pre-drill from the side.
If you're using particularly heavy tiles, feel free to run your anchors into the upper rail. That completely eliminates any concern of damage.