Sgin in with Google for web: switching account changes the SESSION on server, but still the same account on Google button

Question

implementation: "Google JavaScript API" with button, without One Tap.
Scenario:
The user had two Google accounts A and B, while already logged in with A, without logging out A account he then switched to B account by Google button, and the server changed the $_SESSION accordingly.
Issue:
After that, the user now has B $_SESSION on the server, whilist Google button still show account A icon.

Tried to logout the user when he switches account, but there don't seem an event I can attach to.