I have observed this in case of both Goat serum albumin and Bovine serum albumin addition to HBSS where the pH of the solution reduced from 7.4-7.6 to 7.2-7.3. Now, looking for the reason.
Hemoglobin's pH is around 7.1 to 7.4. While preparing Hank's b balanced salt solution, you can adjust the pH by adding HCI or NaOH. I think after your observation of this decrease, you can add more NaOH while preparing Hank's solution to reach the desired pH.