You‘re partially correct. Adding reducing agents will cause $O_2$ to be converted to $H_2O_2$, as thiol groups are turning from $SH$ to $S$-$S$ (forming dimers). In a second reaction, further thiols may reduce $H_2O_2$ to $H_2O$, (but H2O2 also may react with $SH$ to form toxic byproducts like thiooxides $SO$).
Intermediates (like $H_2O_2$ or $O_2^-$) might get reduced to $H_2O$ by subsequent reactions with thiol groups, Enzymes or spontaneous dismutation (Kiley & Stolz 2004, Aires et al. 2008)
$O_2$ + 2 $SH$ -> $H_2O_2$ + $S$-$S$
$H_2O_2$ + 2 $SH$ -> 2 $H_2O$ + $S$-$S$ (see NG et al. 2007, DTT Assay Wang et al. 2018)
However, while the first reaction is very probable, the second reaction is less probable (some even argue that it is too unlikely to have an effect)
The second reaction might depend on concentration. Usually cell culturing protocols are designed by trial and error. So it’s based on testing multiple concentrations to find out the amount that yields the highest culture viability. I can only speculate that e.g. the right concentration hits a sweet-spot. That sweet-spot might lie between production of toxic thiooxide ($SO$) and oxygen reduction. But that depends on a lot of factors like organism and other culturing conditions.
Cell Cultures are in Generally too Oxidative; Reducing Agents might Help no Matter the Exact Reaction Path
Oxygen is a general problem in many cell cultures (Jagannathan et al. 2017). Even for human cell cultures, 20% $O_2$ is not physiological and introduces a background of oxidative stress (it even increases mutation rate).
To describe aggressive oxidative features of oxygen, it's useful to use the more generalized term „reactive oxygen species“ (ROS) instead of "oxygen", since redox potential doesn‘t care which exact compound acts as an electron donor. By referring to ROS, it‘s not necessary to keep track of exact oxygen-compounds.
The main point is that in the end, some biomolecule gets damaged by oxidation and the probability for that increases with high $O_2$ -levels. Hence, reducing agents could increase viability by scavenging any kind of oxidative species from the medium. And it makes sense to assume that one of the end products might be $H_2O$.
„the higher the potential, the higher the dissolved oxygen in medium“.
I think the wording is misleading, since high redox potential is a consequence of oxygen being present, not the other way around (as that would imply something like high redox potential attracting atmospheric oxygen into water). I speculate that the author meant that dissolved (organic) compounds tend to release $O_2$ (or rather any reactive oxygen species (ROS)) more often in an oxidative milieu.
