At the onset of exercise, the sympathetic nervous system causes heart rate to elevate and blood vessels to constrict
This part of your reference may refer to an initial response to starting exercise (or a fight or flight response).
Generally, to get ready for exercise, blood vessel constriction will cause more blood to be in more rapid circulation.
There is a lot of compliance (flexibility) in blood vessels (especially veins) that can be modulated by vasoconstriction.
A general constriction of the veins (or spleen) will put more blood into more rapid circulation so more oxygen can be carried to where its needed.
For example veins in your legs will normally be somewhat expanded (large diameter) so they will hold more blood and it will flow through the larger diameter vessels more slowly. Constrict those veins and that blood will go elsewhere (presumably where needed) and the blood returning through those veins will pass through them more quickly (smaller diameter) and return to get reoxygenated.
These could also be constriction of arteries going to body parts not needed at the time.
The spleen is also a storage place for blood (in some animals anyway).
In addition, the contraction-relaxation cycle of muscles will provide local high and low pressure on vessels going to and from the contracting muscles. This can help get blood depleated of oxygen out of the muscles so it can be reoxygenated.