Once learning that the Doctor was poisoned, Koschei hurried to the complex to find him. He knew this wasn't the Doctor he'd known in his universe, but the Doctor was the Doctor and he deserved to be helped. And Koschei wasn't going to let this poison work if there was anything he could do about it. While obeying traffic signs and such, Koschei hurried all the way to the complex, suddenly wondering why he was staying so far away from it. From the looks of the abandoned building he'd arrived in, someone was living there, and it didn't take long to discover it was, in fact, another version of himself. It was all very confusion, but there wasn't much time to dwell on the intricacies of such things.
Finally arriving at the complex, he went inside, making his way to the Doctor's room. The complex was fascinating, actually. All the people that had been displaced from their own realities lived here in one spot. Genius, actually. Keeping everyone who could potentially help in the war going on in one spot, and the protections were impeccable. Definitely kept everyone inside safe from the dangers of the world outside.
Finally finding the Doctor's apartment, Koschei entered without knocking, as the Doctor had told him. He took only enough time to close the door behind him. After all, he didn't want anyone potentially snooping on them should the Doctor start regenerating, or simply just start dying. No, they needed some privacy for this.
"Doctor, I'm here," he announced, rushing over to his friend. "Tell me what I can do." He had a good thought that whatever poison was used, it was probably unique to the world the Doctor had been in and not universally shared by the various Gallifreys in various realities. He did make quick note of the red skin on the back of the Doctor's hand and knew this was very bad.