Flush mounted registers require the installation of a frame so floor register will be removable
How to install a frame in a new floor installation
Center frame over duct hole opening to determine outside dimensions surrounding tiles will be brought to.

Bring surrounding tiles to the edge of frame leaving enough space to grout or caulk.
When setting tiles apply thinset adhesive to the edge of the duct hole press centered frame into thinset adhesive until top edge of frame is flush with the surface of the surrounding tiles.
Make sure to clean out any oozing thinset adhesive from inside frame so damper can fit into duct hole and register will seat properly into the frame.
How to install a frame in an existing floor
Center frame over air duct and mark outside dimension of frame, allow an extra 1/8 for grouting or caulk. Cut on mark no deeper than the top of setting bed. Remove this material from marked area. Set frame in cleared area dry to be sure placement is correct (top of frame is flush with top surface of surrounding tiles and there is room for adhesive under frame. Refer to pictures above). Apply enough thinset adhesive to edge of duct opening so top edge of frame is flush with the surface of the surrounding tiles.
Make sure to clean out any oozing thinset adhesive from inside frame so damper can fit into duct hole and register will seat properly into the frame.