The timeline is faulty. The design of the sweat experiment and Inks presence in the tower are separated by weeks. The time stamp is very subtle. When Kelly is searching Lizzy's apartmentand rattles the sweat jars, Lizzy says hey, tat is like three weeks worth of work. So, there seems to be a break of three weeks from the testing of the theory to the tagging.

The biters also take the dead bodies from the apartment much earlier in the story. It happens when they get the fuel tanker. This has to also occur early in the story, in my opinion. The food and water dispensers are for days, not weeks and Lady is alive and well

As for Ink's visit to the tower, is that retaliatory for the tagging and attack on his arena? I do not know. He clearly attacked Dunbar. He must have felt threatened by it much as the mallers did