  We present an extended version of the Constant Time Lag analytical approach
for the tidal evolution of circumbinary planets introduced in our previous
work. The model is self-consistent, in the sense that all tidal interactions
between pairs are computed, regardless of their size. We derive analytical
expressions for the variational equations governing the spin and orbital
evolution, which are expressed as high-order elliptical expansions in the
semimajor axis ratio but retain closed form in terms of the binary and
planetary eccentricities. These are found to reproduce the results of the
numerical simulations with arbitrary eccentricities very well, as well as
reducing to our previous results in the low-eccentric case. Our model is then
applied to the well-characterised Kepler circumbinary systems by analysing the
tidal timescales and unveiling the tidal flow around each different system. In
all cases we find that the spins reach stationary values much faster than the
characteristic timescale of the orbital evolution, indicating that all Kepler
circumbinary planets are expected to be in a sub-synchronous state. On the
other hand, all systems are located in a tidal flow leading to outward
migration; thus the proximity of the planets to the orbital instability limit
may have been even greater in the past. Additionally, Kepler systems may have
suffered a significant tidally induced eccentricity damping, which may be
related to their proximity to the capture eccentricity. To help understand the
predictions of our model, we also offer a simple geometrical interpretation of
our results.
