Order at the end of your turn?

[Lupine]

So, I'm planning the BBEG for my group. The BBEG has the spells Immolation and Psychic Scream.

With Immolation, the target makes a dex save to avoid the spell altogether, and then repeatedly makes dex saves at the end of their turn to avoid additional damage. It is concentration.

With Psychic Scream, the target makes an Int save to avoid a lot of damage and getting stunned. At the end of every turn, the creature remains stunned, until it succeeds on the save (Which will be really tough for some party members in my group, esp the pali with 8 int, and the BBEG having a DC19 spell save). It is not concentration.

So, obviously, the BBEG is going to cast Psychic Scream first, because it allows them to dominate the action economy by stunning a few people. Then, those stunned people become prime targets for Immolation, because stunned targets automatically fail dex saves.

So here's the problem: the Immolation save happens at the end of the creature's turn. However, the Scream save also happens at that same time. Potentially, if the creature succeeds the Scream save, they could avoid the Immolation save, and if they fail the Scream save, they automatically fail the immolation save.
What order should the saves be in?

My inclination is that the highest level save goes first, but will this break anything?

[PhantomSoul]

If you use Xanathar's (or tweets) as guidance:

In rare cases, effects can happen at the same time, especially at the start or end of a creature's turn. If two or more things happen at the same time on a character or monster's turn, the person at the game table - whether player or DM - who controls that creature decides the order in which those things happen.

(p. 77)

Alternatively, having it be in the order a creature is affected (requires remembering or keeping track) or some other consistent system makes sense. One issue you could encounter is that abilities don't have comparable power levels (so you'd need a system/guideline for that), or you might want to decide based on the source's power level (e.g. spellcaster's spellcasting ability) instead of the spell level itself.

[Segev]

Yeah, letting the players choose the order seems the most fair. 5e expects you to save out of effects pretty quickly.