In Rhode Island. Windy location. 7 ft by 6 ft L shaped lattice trellis/fence. Clay/rock soil.
Should we have the posts placed in the hole with cement?
I believe that in RI, just like in MA you want your fence posts sunk below the frost line, so the answer is yes. Use Sonatube and go at least 3-4ft deep and set them in concrete.
The 3 to 4 foot depth may be needed for corner posts or those on either side of a gate, especially in an extremely windy location, but is excessive for the line posts. Two feet in the ground is enough. The usual recommendation is to tamp the bottom of the holes well, then add a minimum of six inches of gravel to the bottom for drainage. Concrete is then poured into the hole, tamped and the top sloped away from the posts to shed water.
You could, if you're really ambitious and love to dig holes, install Sonotubes and above ground hardware to hold the posts. This would give as close to a rot-proof installation as possible, but would require a lot of concrete and a huge excavation project. Otherwise, Sonotubes are not needed at all. Pressure treated posts listed for ground contact and installed as indicated in the first paragraph above will last for a very long time.