If you're properly pre-exhausting the chest, there's no way the tris fail first afterwards. You're possibly not using enough intensity on the pre-exhaust part. With high intensity, chest will already be fried before getting to the other exercise.
Also look at the form used on the compound exercise, see if there are alternate grips that might take the emphasis off the tris. If not, consider different exercises.
Lastly, try 2 different forms of pre-exhaust:
1/ Superset: 1 Isolation exercise followed immediately by 1 compound exercise.
2/ An isolation exercise done for multiple sets, with rests in between sets. Following completion of this, do the same with the compound exercise, also done in standard set form with rest in between each set.