While Erin is telling Ike and Corabeth that Grandma is teaching Elizabeth to cook, Elizabeth puts the lid on Corabeth's pot of stew. The shot changes and the lid is once again off the pot. While Jason is inviting Ike and Corabeth to stay for supper, Elizabeth puts the lid on the pot again.
Since 1907 the test for TB was a tine test, a skin jab, that required 48-72 hrs waiting before the patient's skin jab area was rechecked for redness or swelling. So there is no way Olivia's Aunt Kate would have driven to the house with the test results.
Olivia is diagnosed with TB following tests she had. As TB is contagious there were no tests carried out on her husband John or her seven children, as TB infections usually spread between family members.