According to the post you linked, paresthesia causes the "falling asleep" notion. According to Wikipedia, there are two types of paresthesia, transient and chronic. Transient paresthesia is the type you are describing.
Paresthesias of the hands, feet, legs and arms are common, transient symptoms. The most common, everyday cause is temporary restriction of the blood supply to an area of nerves, commonly caused by leaning or resting on parts of the body such as the legs; other causes include conditions such as hyperventilation syndrome and panic attacks.
Other places like this link mention that parethesia is caused by:
• Obdormition: Obdormition is a numbness caused by prolonged pressure on a nerve,
such as when a leg falls asleep if the legs are crossed for a prolonged period. It
disappears gradually as the pressure is relieved (1).
• Whiplash: Paresthesias in the upper extremity may occur after
whiplash injury (2), a type of cervical soft tissue injury (3). Pujol
et al showed that 13% of patients with whiplash had associated
paresthesias (4). Recovery usually arises within 6 months after injury
(5).
• Hyperventilation syndrome: Paresthesia constitutes 35% of presenting
complaints in patients with hyperventilation syndrome (6) and may
begin after as little as threeminute of hyperventilation (7). After
increasing the depth or frequency of respiration, www.intechopen.com72
Paresthesia the alkaline shift produced selectively increases Na+
conductance and ectopic discharges in normal cutaneous afferent nerves
can be induced (8). Other electrolytes, i.e. magnesium, potassium,
chloride, phosphate and bicarbonate, also demonstrated significant
changes in concentration (7).
• Panic attack: Paresthesiae of the mouth, hands and feet are common,
transient symptoms of the related conditions of hyperventilation
syndrome and panic attacks. Ietsugu et al demonstrated that
paresthesia can be used as a reliable indicator of severe panic
attacks (9).
• Transient ischemic attack (TIA): TIA may be manifested by
paresthesias. Several reasons may cause TIA such as thrombosis,
embolus, intravascular debris and blood vessels disruption. Perez et
al. reported the initial manifestation of cardiac myxoma can be
paresthesias caused by TIA (10). Post-ischemic paresthesia occurs when
hyper polarization by the Na+/K+ pump is transiently halted by
elevated extracellular K+. The electrochemical gradient for K+ is
reversed and inward transport of K+ triggers regenerative
depolarization (8).
• Seizures: Paresthesia may happen during and after a partial seizure
(11). Treatment of seizures with vagus nerve stimulation can also
trigger paresthesias and is considered an adverse event associated
with this treatment modality (12).
• Dehydration: At around 5% to 6% cumulative water loss, paresthesia
may occur.
• Insufficient blood supply: Circulatory disorders could lead to
transient or chronic paresthesia.
As you can see, there are many causes for paresthesia. The most common is the pressure on the nerves and the loss of loss supply.
Usually, the feeling quickly goes away once the pressure is relieved. But in your case, the paresthesia is delayed because it's caused by restriction of blood flow. Because it is caused by restriction of blood flow, it may take time for the blood the reach the area and oxygenate the nerves.
Why does it get worse? Well, because the action of standing up causes the blood pressure and heart rate to increase, decreasing blood flow to the nerves (read the abstract of this). Another reason is that when standing up, there is increased pressure on the nerves, causing paresthesia. Together, these effects, may increase paresthesia for a few seconds. But when the blood flow becomes normal and the pressure on the nerve decreases, the paresthesia goes away.
There you have it! Nice and concise hopefully... @Daniel if you have more questions, you can ask them by adding a comment to this post.