When I put my little, cylindrical coffee straw into my coffee, the liquid immediately rises about half a centimeter up the straw without provocation. This is also the amount of coffee that the surface tension of the coffee will allow to stay in the straw when removed from the liquid in the cup.
Keep in mind that all the while, the top end of the straw is open.
Why does the level of the liquid in the straw insist on being higher than the level of all the liquid in the cup?
Just to extend my comment about Capillary action which is the reason for the liquid rising through the capillary (straw in your case), I show this animation of how the diameter of the capillary (d) effects the height of the liquid (h) that rises above the contact surface.
The relation of $h$ and $d$ used to simulate this is taken from wiki page which is $$ h=\frac{4\gamma cos\theta}{\rho g d}$$
It is for water and with the value of all constants substituted we get $$h\approx \frac{2.96\times10^{-5}}{d}m$$
The diameter varies from $0.3mm$ to $2mm$
Also the answer to this question would make this true for your coffee as well.
You have 3 different materials in your experiment: a liquid (coffee, could be water), a solid (plastic straw) and a gas (air). You have interfaces between all three: liquid-air, liquid-solid and solid-air. In the case of the plastic of your straw, adhesion forces are stronger between plastic and water than plastic and air: so a force will tend to make the water spread on the plastic. This force balances with gravity to set the height of the capillary rise.
The liquid rises due to surface tension. In this case the adhesion between liquid and cup material Is higher than cohesion between liquid molecules. So it is higher than liquid in cup. I think the liquid in the straw that remains after removing will be lesser than the liquid that you saw rising while in the cup. Try for transparent liquids. The liquid in the case you mentioned is purely due to adhesion and not surface tension forces.
