How confident should one typically be in blood tests ordered by a hematologist with oncology specialty showing no signs of cancer?

Very..... Despite the preachings of the american cancer society, and their slogan...."the cure is just around the corner, " not a lot of advances have been made in cancer treatment in the past 30 years. Sure, certain limited types of cancer have better survival rates, but most do not. Oncologists are still infusing the same "rocket fuel" they did 30 yrs. Ago, with poor results. Take your above dx. Tothe bank.
One of several tools. Blood testing to detect cancer recurrence is just one of several tools. Close follow-up with your cancer care specialist is required. The health care specialist will listen to you, examine you, and order appropriate tests to determine the status of your cancer. Blood testing is frequently not reliable, but depends on the type of cancer and test being performed.