I was trying to catalog which realms have which tier 5 mats and found noble bismaltus, noble hollow, and einaidia in an ascended herbarium forest the first time and then 2x Dulcet Lapis deposits and a noble hollow the second time after resetting the realm
So tier 5 materials must pertain to a certain biome but they will be random within each astrolab, herbarium, gloom etc realm type.
I think lorewise, the minor and major cards played prior to traveling affect the next realm but I haven't noticed any correlation to that effect in practice