C of G
There was quite a lot about C of G about a year ago in Thread 5 #394 ...etc. Some of it IIRC implied that fuel was transferred " in chunks" forward for use in flight whilst keeping the C of G within the normal "in flight limits" by some margin. I would guess that during the transfer of each "chunk" the aircraft would respond to the change of C of G with a change of speed or F/L , normally adjusted by A/T and A/P - but if these are not available then manual control would seem more sensitive.
( On a York hand flown, it could feel as though the passengers were playing cabin football, with a goal at each end of the cabin !)