Trex and other composites seem to have more movement than I'd be comfortable with unless it was mechanically fastened.
The deck at our house is made entirely of Trex, from the decking and posts to the railings and balusters and it does like to "move". The width of the Trex pieces do not seem to change much with moisture like wood does. But the length of the pieces do seem to get longer and shorter depending on the temperature.
This has led to some of the longer deck boards buckling a bit during the summer and then contracting during the winter. Everything is held in place with Trex color matched screws, and it seems like the screws on the ends of the longest boards shear off at the joint between the bottom of the boards and the joists underneath them.
The shorter the Trex pieces are, the less they do this. It only seems to happen on the longest ones.
For that reason, I don't think I would put Trex down using adhesives as it might break the bond and make the boards loose if you don't have some type of mechanical fastener like nails or screws.
Jim