Is your project location set to somewhere in Australia by any chance? Your diffusers could be configured for global orientation to the wrong coordinate system.
(OK, done laughing now 🙂
This is actually an easy mistake to make when placing hosted families.
It sounds like you may not be using the correct "placement mode" for what you are trying to accomplish. When you select the "Air terminal" button on the design bar and then choose "Square Supply Diffuser - Hosted: " then 3 buttons should appear on the options bar, next to the properties button (you may have to hover over the active view to make these buttons appear). The 3 buttons are for:
1. Place on Vertical Face - this mode will place the diffuser on the Host Face that you select, oriented vertically, at the defualt elevation of the diffuser (4ft in this case). This mode is intended primarily for placement on a wall. Note: if you select the ceiling grid as the host, the difusser will be placed oriented vertically at the (x,y) location you selected on the host(ceiling), but at the default elevation of the diffuser family.
2. Place on face - This mode will place the diffuser directly on the host face at the the location that you select. Default elevation is not applicable in this case.
3. Place on Work Plane - This mode will place the diffuser on the current work plane at the (x,y) location that you select.
I suspect that you probably used Mode 3 (Place on Work Plane), and that your work plane is located at floor level. The easiest way to place the diffuser on the ceiling grid is to use mode 2 (Place on Face).
Hope this helps.
Jason