  Thomas and Williams conjectured that rowmotion acting on the rational
$(a,b)$-Tamari lattice has order $a+b-1$. We construct an equivariant bijection
that proves this conjecture when $b\equiv 1\pmod a$; in fact, we determine the
entire orbit structure of rowmotion in this case, showing that it exhibits the
cyclic sieving phenomenon. We additionally show that the down-degree statistic
is homomesic for this action. In a different vein, we consider the action of
rowmotion on Barnard and Reading's biCambrian lattices. Settling a different
conjecture of Thomas and Williams, we prove that if $c$ is a bipartite Coxeter
element of a coincidental-type Coxeter group $W$, then the orbit structure of
rowmotion on the $c$-biCambrian lattice is the same as the orbit structure of
rowmotion on the lattice of order ideals of the doubled root poset of type $W$.
