  The lightest hidden-bottom tetraquarks in the dynamical diquark model fill an
$S$-wave multiplet consisting of 12 isomultiplets. We predict their masses and
dominant bottomonium decay channels using a simple 3-parameter Hamiltonian that
captures the core fine-structure features of the model, including isospin
dependence. The only experimental inputs needed are the corresponding
observables for $Z_b(10610)$ and $Z_b(10650)$. The mass of $X_b$, the bottom
analogue to $X(3872)$, is highly constrained in this scheme. In addition, using
lattice-calculated potentials we predict the location of the center of mass of
the $P$-wave multiplet and find that $Y(10860)$ fits well but the newly
discovered $Y(10750)$ does not, more plausibly being a $D$-wave bottomonium
state. Using similar methods, we also examine the lowest $S$-wave multiplet of
6 $c\bar c s\bar s$ states, assuming as in earlier work that $X(3915)$ and
$Y(4140)$ are members, and predict the masses and dominant charmonium decay
modes of the other states. We again use lattice potentials to compute the
centers of mass of higher multiplets, and find them to be compatible with the
masses of $Y(4626)$ ($1P$) and $X(4700)$ ($2S$), respectively.
