ω/n vs. e phase space, reproduced from Leconte et al. (2010) Fig. 1. Here, ω = Ω_p or Ω_BD. The planets are in pseudo-synchronization so Ω_p/n remains on the black solid line, thus the planetary tide always contribute in making the semi-major axis and eccentricity decrease. If the eccentricity is  ~ 0, we can see that if Ω_BD/n > 1 the BD tide contributes in pushing planets away and if Ω_BD/n > 18/11 ~ 1.64, the eccentricity increases.