It's been my experience in Boeing a/c (14,000 hrs) that the fuel total is slightly low in the climb and shortly after level off. After level off it typically adjusts closer to actual fuel on board.
Eg - close to top of climb today fuel was already -700 lbs. After approx. 20 minutes at cruise we were down to -300 lbs. There's no way we were burning 1200 lbs less per hour which is what that fuel change would require.
No observed, repeatable, issues with fuel totals related to center tank fuel use on 737-800's(700+ hrs).