strange firefox behavior with X tunneling via ssh

If I'm on system a as user a and I ssh (using X tunneling via ssh -XC)
into system b as user b and run firefox as user b so that firefox
is displayed on system a over X, then if I run firefox on system a as
user a (from the gui) firefox starts with user b's bookmarks and other
contextual info (cookies, etc.)!

Why is this happening?
% Randy Yates % "She tells me that she likes me very much,
%% Fuquay-Varina, NC % but when I try to touch, she makes it
%%% 919-577-9882 % all too clear."
%%%% <yates@xxxxxxxx> % 'Yours Truly, 2095', *Time*, ELO