I will be answering my own question now since I finally seem to grasp the physiology and just in case of someone also being confused :) I can still be corrected though
So the sympathetic nervous system constricts SPECIFIC arteries and constricts ALL veins of the systemic circulation. Let's assume that this person is in fear.
So, I used to wonder, since constricting a tube, there will be less blood flow through it per unit time, so how does constricting the veins give rise to more venous return? So this is the thing, the veins actually store blood during rest! Also, remember that veins are not completely circular like arteries! They are like flattened circular tubes. So now when we constrict these veins, we make the tubule more circular and we propel more of that blood that was hanging in the veins because the movement of blood in the veins is slow and moves against gravitational force. Also, the resistance of the veins increases BUT so does the pressure. So you might think that the increase in resistance does not allow the desired venous return, BUT, the increase in pressure overweighs the increase in resistance. The increase in pressure produces this pressure gradient between the veins and the right atrium; the blood moves down the pressure gradient and it moves down this gradient faster as the gradient rises.
The sympathetic nervous system releases catecholamines, that being norepinephrine and epinephrine. There are these receptors with which these hormones interact with. In one case, when this hormone interacts with one type of receptor, it cause vasoconstriction, and when it interacts with another type of receptor, it cause vasodilation.
There are CERTAIN adrenergic receptors in CERTAIN places. In the veins, there are the receptors that cause vasoconstriction, specifically, these receptors are alpha 1 adrenergic receptors. Then we also have beta 1 adrenergic receptors in the heart, where when these interact with the hormone, they cause vasodilation. So we need vasodilation in the coronary arteries so that more blood can flow through them and allow the heart to work harder as the blood brings to the cells its metabolic needs, such as oxygen, glucose etc.
We also have beta 2 adrenergic receptors found in skeletal muscles, which after an interaction with the hormone, causes vasodilation and increases perfusion. As a result, allowing the muscles to work harder as they get more blood carrying its metabolic needs.
All in all, alpha adrenergic receptors cause vasoconstriction and beta adrenergic receptors cause vasodilation. Epinephrine excites more of the beta adrenergic receptors of the vessels; epinephrine has a slight vasodilator effect because epinephrine excites more of the beta adrenergic receptors of the vessels. Norepinephrine excites more of the alpha adrenergic receptors of the vessels. But high levels of epinephrine causes vasoconstriction of for example the skin arteries because there are more alpha adrenergic receptors in the skin arteries. Also, high levels of epinephrine causes vasodilation of the coronary arteries as there are more beta adrenergic receptors. Low levels of epinephrine causes vasodilation of for example the skin arteries as the beta adrenergic receptors have more affinity for epinephrine as the epinephrine cannot be easily stolen by the alpha adrenergic receptors to cause an overall vasoconstriction.
During fear, the sympathetic nervous system is trying to pump more blood to the brain and skeletal muscles so that we are more conscious and more ready to fight or run away. Therefore, for example, the skin does not need much blood in this situation, and hence the blood moves away from the skin towards the heart to be pumped to the brain. The arteries of the skin contain mainly alpha 1 adrenergic receptors, hence vasoconstriction occurs during high levels of epinephrine, and less blood is available for the skin. This is one reason why you get pale during fear.
Also, one very important difference to bear in mind, is that constriction of arteries DECREASES blood flow because it decreases perfusion, and the constriction of veins INCREASES blood flow because it increases venous return.
In conclusion, "sympathetic activation can cause arteries to dilate or constrict depending on the receptors it acts on. Sympathetic activation causes constriction of arteries in the skin, but it also causes constriction of veins in the systemic circulation, which improves venous blood flow and thus venous return to the right atrium of the heart. Sympathetic activation almost always improves the pumping action of the heart, whether its effect is on the arteries (e.g. dilation of the heart arteries and the resulting increased blood flow to the myocardium and increased pumping activity of the heart chambers) or on the veins (constriction of the veins and the resulting improvement in venous return, an increase in end-diastolic volume and an increase in the stroke volume of the heart chambers)" (My Professor).
And the very very narrowed down conclusion, is that THE SYMPATHETIC NERVOUS SYSTEM IS TRYING TO CENTRALISE THE BLOOD TO THE BODY WHERE IT IS NEEDED THE MOST, AND IT DOES THIS BY CONSTRICTING THE ARTERIES OF AN AREA OF THE BODY WHERE BLOOD IS NOT NEEDED MUCH, BY CONSTRICTING THE VEINS OF THE SYSTEMIC CIRCULATION TO IMPROVE VENOUS RETURN, AND BY DILATING THE ARTERIES OF AN AREA OF THE BODY WHERE BLOOD IS NEEDED THE MOST TO IMPROVE PERFUSION.
That was long but pretty amazing.
Sources: Wikipedia (Adrenergic receptor), Guyton and Hall medical Physiology Textbook, My Professor, Alila Medical Media (Mechanisms of Venous Return, Animation)