Do the following. The wait for 0 ns follows the assignment to SB_int to allow SB_int to update.
stim : process
begin
SB_int <= NewID("COUNT_SB");
wait for 0 ns; -- let SB_int to update
report ("SB_int: " & integer'image(SB_int.Id));
i_up_or_down <= '0';
push(SB_int, 2);
. . .