The objectively funniest possible way for Darth Vader to have perceived Ahsoka getting yoinked into the portal at Malachor is for her to disappear into thin air. One second he's swinging his lightsaber at her, the next she's gone. He has no idea what happened. Is she dead? Did he somehow vaporize his Padawan former apprentice? He can't feel her presence in the Force anymore, so he decides that must be it.
But over the next few years, he notices a few...anomalies. Little things. Nothing certain, but the evidence is there and he knows Ahsoka's work when he sees it - there can't be that many orange Togrutas with blue and white montrals running black ops against the Empire. Somewhere, somehow, she's alive. The Force hums in agreement.
The A New Hope happens. He swings his lightsaber at Kenobi and the old man disappears into thin air.
Vader has seen this trick before. He won't be fooled by it twice.
His suspicions are confirmed when he senses his old master's presence guiding the boy who destroyed the Death Star: Obi-Wan Kenobi is still alive.
And the old traitor never taught Anakin how to teleport, even though he clearly took the time to teach Ahsoka!
Vader seethes with unimaginable rage.