Multidimensional screening and convexity of the surplus/rent function
First, it's important to be clear about what Rochet proves. In theorem $1$ of Rochet (1987), he shows that cyclical monotonicity is equivalent to the implementability of a mechanism for general environments (i.e. arbitrary allocation/type spaces). (See the statement of theorem $1$, or a standard text such as Borgers (2015), for the definition of cyclical monotonicity.)

The convexity result (proposition $2$) applies to the case when $u(x,\theta)$ is linear in $\theta$. In this case, we have that

$$ V(\theta) = \max_{\theta^\prime} \, u\left(x\left(\theta^\prime\right),\theta\right) - t\left(\theta^\prime \right) .$$

The convexity of $V$ follows from the fact that it is the maximum of a family of linear functions. I'm not sure there's much more intuition to be given here, but a simple drawing may help. (That is, draw two straight lines that intersect. The maximum over the two straight lines will be convex, while the minimum will be concave.) This may also help.