Tyson's explanations are often wrong. Possibly the most inaccurate pop science celebrity who has every lived.

Not remotely the same league as Richard Feynman.

Sagan's critics were wary of pop science. Would the need to entertain come before rigor and accuracy? And their fears were realized with Tyson. Possibly the sloppiest, most inaccurate pop science celebrity ever.

Tidal influence can keep an object oriented along the local vertical and keep the same face towards the primary. See, for example, Phobos. Or most the moons in our solar system.

This is especially true if an orbiting object has attached to a tether. Gravity gradient stabilization can keep a tether aligned to the local vertical.

As others have mentioned, The Hermes didn't follow a Hohmann trajectory. It is an ion propelled craft capable of 2 mm/s^2 acceleration. A very weak thrust but powerful in that it can sustain this acceleration for looooong burns.

If just the sun is accounted for, Andy Weir's trajectories are okay (I believe). However putting planets in complicates things. Ion engines really suck at climbing in and out of deep planetary gravity wells.

Neil deGrasse Tyson's trailer for The Martian had Hermes leaving low earth orbit and arriving in Mars orbit 124 days later. Which is nonsense. With 2 mm/s^2 acceleration it would take 40 days to spiral out of earth's gravity well. Not only does this wreck the 124 day trajectory Weir so painstakingly calculated, but most the slow 40 day spiral would be in the Van Allen belts. This astronauts would be killed by radiation.