Where would the soul of someone who worshiped the tribunal go?

Oops misspelled Worship in the title I feel like an idiot.

Dreamsleave most likely i suppose

This. The Tribunal don't have a presence in Oblivion like the Daedric Princes, and while the Temple doctrine reveres certain Daedric Princes, remember that these Princes are not the ones being worshiped.

Due to Dunmer ancestor worship (they summon undead to guard their family tombs), the dead Tribunal worshippers go most likely to the Dreamsleeve

Your earthly remains will be buried in the ancestral tomb or ghostfence of your family or House, or possibly brought to Necrom, the City of the Dead. Or perhaps a combination; some of your bones may be taken by the House that your family serve.

That may have been irrelevant. Back on topic. I believe the spirits of Dunmer ancestors at least in part stay on Nirn to aid and serve their House and/or family. Some Dunmer can even summon their ancestors. The spirits stay in ancestor tombs or behind 'waiting doors'. When you think about it the spirits must be everywhere in Morrowind, as they may have been doing this for thousands of years. Is this a scheme designed to invalidate the dreamsleeve by draining it of souls?

It means, most likely, that some souls are bound to the tombs to guard them, and Dunmer can summon them from there when they are needed. Security I think, nothing to do with a conspiracy

Come on people. Can you point to any Tribunal temple literature that makes mention of the Dreamsleeve? If no, then I feel it is irrelevant to their religion.

I think a useful source for this is the prayer that Vivec says to the afraid or dying in the 36 Lessons:

I take this to mean that the fundamental laws of the afterlife enshrined in Tribunal religion have not changed since the old Velothi ways, and the Good Daedra have sway over the passage of Dunmer souls, although the Tribunal have influence over their anticipations - possibly "the fire is mine: let it consume thee" means something like "dedicate your dying soul to me and I will ensure you comfort in the next world". Likely the "House of Boet-hi-Ah" is seen as a peaceful rest, whereas servitude in the ghostfence or as an ancestral spirit is an unpleasant experience, possibly part of a tradition that predates the Tribunal themselves.

As far as I can tell, the Tribunal are the gods of the living, not the dead. An exception to this is when Vivec describes himself as the "Psychopomp" - while the domain of the dead is not strictly his, he has the power to conduct spirits through it. I would be inclined to combine this knowledge with what we know of the "waters of Oblivion" and say that while the "dreamsleeve" is not a part of the Dunmer religion, the Houses of the Anticipations (watched over by the Tribunal) play a similar role in facilitating reincarnation.

However, one of the lessons enshrined in Vivec's teaching is that death is not always the end for souls: the ideal is to retain your agency and selfhood outside the boundaries of alive/dead, real/unreal. This links in to his teachings about The Tower.