Use of pipette during experiments for determination of oxygen by Winkler's method
[...] the pipette tip should be well below the surface of the solution [...]


Usually, one would indeed keep the pipette above the solution to avoid that a (minor) part of the solution forms a drop (or film) on the tip of the pipette and is carried away.

Here, when the amount of oxygen dissilved in the solution is to be determined, another effect prevails. 

If you add your reagents from greater height, you might create a splash, just like throwing a rock into a lake. As a result, you will mix some oxygen from the gas phase into the solution, which might taint the measurement.