When applying the boolean masking countermeasure to a cipher which uses an S-box $S$, a way to handle this nonlinear operation is to recompute a new S-box $S'$ such that $S'(x \oplus r_{in}) = S(x) \oplus r_{out}$ (see, e.g., this paper).
On the other hand, for processors using cache techniques, look-up tables have been proven vulnerable against timing attacks (see this paper). Therefore, it is recommended to use regular implementations (e.g., bitsliced implementations).
My first impression is that the masking technique described above also acts as a countermeasure against the timing attack introduced by Bernstein (as the look-up table accesses do no longer directly depend on the internal state, but also on a random mask $r_{in}$). However some works study bitsliced masked implementations to prevent timing and power side-channel attacks (see, e.g., this paper).
So my question is, does a masked look-up table as described above (assuming $r_{in}$ and $r_{out}$ are renewed at each execution) also prevent from cache timing attacks? Are there any published papers on the link between this countermeasure and timing side-channels?