FROM MY EXPERIENCE - No, the chambers do not get harder if say I choose Ares consistently in a trail of the gods chamber.
On the note of conflicted reports.... TVTropes directly contradicts themselves in the same section the above quote comes from:
- Adaptational Nice Guy: In Greek mythology, the Olympians are known for being vindictive and petty. While they certainly become offended if you side against them in the Trial of the Gods, they get over it after surviving. Otherwise, they're nothing but supportive towards Zagreus and are eager to meet him in person.
- Easily Forgiven: During a Trial of the Gods, whichever Olympian you don't choose becomes offended by the spurn and summons waves of empowered monsters, but once you clear them they are quick to forgive you and give up a Boon anyway. That said, they will begin to notice if you continue to reject them several times in a row, making their Trials progressively harder until you choose them.
Having played the game several times and participated in multiple trials, no the rooms tend to maintain their difficulty curves, HOWEVER IF YOU HAVE MULTIPLE TRIALS, there is a chance that there is "increased difficulty from a spurned god" but it would be measurable to the "difficulty" of the world. I.E. if you have a trial in Tartarus between Ares and Athena and choose Ares, and later you have ANOTHER Ares/Athena trial, then Athena's attacks could be slightly more than before but the trial would not be more "difficult" than if it was the first trial
NOTE: the devs are also publishing updates to the trial of the gods attacks so there is some room for failure as this answer and others age.