The answer is in Eqn. 8 of the referenced paper, and its surrounding paragraph:
The overall complexity [of simulating $e^{-i(A+B)t}$ using the interaction picture formalism and the Linear Combination of Unitaries (LCU) method] depends on the value of $\lambda$, which is the sum of the weights of the unitaries when expressing $B$ as a sum of unitaries. To simulate within error $\epsilon$ the number of segments used is $\mathcal{O}(\lambda t)$, and [a cutoff energy introduces additional poly-logarithmic factors]. The complexity in terms of LCU applications of $B$ and evolutions $e^{-iA\tau}$ is therefore ... $\mathcal{\widetilde O}(\lambda t) $.
After Eqn. 13 they further argue that $\lambda$ in the interaction picture is fairly bounded by $\mathcal{O}(\eta^{5/3} N^{1/3})$, with $\eta$ the number of electrons and $N$ the number of basis orbitals. Around Eqn. 18 they argue the effective complexity of implementing each step is $\mathcal{\widetilde O}(\eta)$. This puts their overall complexity at $\mathcal{\widetilde O}(N^{1/3}\eta^{8/3}t)$, as claimed in the abstract.