You are correct.I'm assuming the answer is talk to you DM.
The answer is always talk to your DM. However, in this instance, there's no specific reason to think otherwise. They are transported to an area where a constant ongoing transit mode they have (they have an innate climb speed) is applicable, and thus would normally be able to use it. If not, and the DM applied the same logic universally, you would have the situation where birds could be teleported to a spot in mid-air, but plummet to the ground because their flying movement is for some reason not applicable.I'm assuming the answer is talk to you DM.
Fiery Teleportation is a short range ability - the caster can see the point they are aiming for, so they can put themselves as close to the ceiling as they like.I would likely allow the wall but might not allow you to suddenly stick to the ceiling. You do not teleport to that space, you teleport to the adjacent space. If you suddenly appear under the ceiling you start to fall before you can grab the ceiling. This is why I can see grabbing the wall and not the ceiling. I could also see something like a DC 15 Acrobatics check to do it.
Fiery Teleportation. The spirit and each willing creature of your choice within 5 feet of it teleport up to 1 5 feet to unoccupied spaces you can see. Then each creature within 5 feet of the space that the spirit left must succeed on a Dexterity saving throw against your spell save DC or take ld6 + PB fire damage.Fiery Teleportation is a short range ability - the caster can see the point they are aiming for, so they can put themselves as close to the ceiling as they like.