Aside "vanishing", both situations had little in common
When Obi-Wan vanished, he had just been struck by a Vader's lightsaber, and left behind in his place were his robes and his own lightsaber. His body literally disappeared from within.
Contrast that to Ahsoka, who from Vader's perspective, had half an arm literally reach over from out of thin air to grab her, pulling her back into nothingness, along with all her possessions.
Vader knew his strike hit in the first scenario, and likewise knew it did not in the second. He knew someone intervened in the second, but had nothing to indicate likewise in the first. Weird for sure, and a little familiar, but too different to jump to the conclusion that he must have been rescued.
But how could they be sure?
I mean, sure, maybe someone reached through the floor and grabbed Obi-Wan's leg and pulled him down out of his robes without Vader seeing. But what then? Do Vader and the Emperor have no way of being certain?
At least as far as what they know to be possible from Ahsoka's situation, they actually do have a way to check. The Emperor could just do what he did last time and call up the world between worlds and see if any Jedi happen to be hiding about.
This leads to two possibilities. Either 1) with the destruction of the temple, access to this space is now closed off, and the Emperor won't be able to see it, which confirms it wasn't involved. Or 2) He accesses it and sees if anyone inside, and knows again whether or not it was used. Even still, given the destruction of the temple, he'd have little reason to suspect it was even accessible or usable anyways.
But what if...
Like you mention, maybe it was some different and presently unknown means of making someone vanish. How could they be sure?
After we've exhausted ruling out the above known means of pulling off this trick, there's really no point for Vader and the Emperor to waste their time speculate further. Maybe he's alive? But probably not. If it later turns out that he is, they'll just revise their understanding of the events and attempt to learn why and how he survived. But until then Occam's razor wins out, and the most likely situation is probably the one that occurred, and he's simply dead.
All of this even still presupposing that the Emperor was unaware of Force ghosts (which seems unlikely, given his and his master's research into surpassing death). If Palpatine did know, then he already knows what happened to Obi-Wan with a great deal of certainty.