Vi's ult gets stopped when she is ulting someone Tahm eats.

Tahm isn't the target. There is no target. The target is not inside Tahm. They are untargetable.

Which isn't the intended function. If she lost her target, her ult stops.

Her ult is unstoppable in terms of being immune to CC. If she ults a Fizz and then he uses his E, her ult stops as well.

No, because no other abilities switch to Tahm after the target was eaten. Things like: tower shots, Annie Q's, Pantheon Q's, Urgot ultimate, etc. Also, Tahm does not take two Karthus ults when he eats someone. There is no reason to assume the target would switch to Tahm.

No, it shouldn't.

Not how her Ult works. One target and that's it. And once her target in untargetable she stops. This isn't a bug.

So what? The target is now untargetable, and Tahm was not the target. Tahm has nothing to do with the target. Same thing as if Fizz jumped on his E.