It’s up to the DM. Magic items are less likely to be destroyed, but again subject to DM ruling.
So on the one hand, the following situation makes little sense to me:
Succumbing to the flames of your immolation spell, the priest crumbles to ash, leaving behind his total mundane cloth robes, untouched by the flames.
The spell isn’t specific here, so it’s going to be up to the DM what burns and what doesn’t. That said, magical items have particular resilience (from the DMG section “Magic Item Resilience”):
Most magic items are objects of extraordinary artisanship, assembled from the finest materials with meticulous attention to detail. Thanks to this combination of careful crafting and magical reinforcement, a magic item is at least as durable as a regular item of its kind. Most magic items, other than potions and scrolls, have resistance to all damage. Artifacts are practically indestructible, requiring extreme measures to destroy.
So a magical item is at least more likely to survive than a mundane item of similar construction. Again, up to the DM.
I’d say your DM’s ruling is within the rules as written, as the rules are somewhat non-specific, but I personally would have ruled that magic items would persist through the flames.