Serotonin - Does being aroused make you sleepy?
According to this article [1], serotonin (5HT) inhibits sexual arousal:

Dopamine is generally facilitative to male sexual
behavior; however, 5-HT is regarded as inhibitory.
Antidepressants of the selective serotonin reuptake
inhibitor class (SSRIs, including Prozac and Zoloft)
impair ejaculatory/orgasmic function and frequently
inhibit erectile function and sexual interest as well.

However, serotonin can also facilitate erections:

Systemic administration of the 5-HT1B receptor agonist
anpirtoline impaired ejaculation in male rats. On the
other hand, stimulation of 5-HT2C receptors with mCPP
impaired ejaculation but facilitated erections in male
monkeys, suggesting an increase in parasympathetic
influence.

Serotonin release also causes sleepiness after ejaculation in males (source):

5-HT is released in the LHA at the
time of ejaculation and promotes sexual quiescence during
the postejaculatory interval

There are many signalling molecules used by the human body that have a different effect depending on the cell type they are detected by and the receptor type they activate.
I would also like to touch on your question about evolutionary benefit. Evolution does not care about you after you have reproduced. As long as an individual reproduces, evolution is &quot;happy&quot;. For example, you think falling asleep after sex is counterproductive on the evolutionary scale? What about Mantises where the female will sometimes eat the male during or immediately after copulation. Falling asleep seems like a pretty small thing compared to that (source):

Although the praying mantis is known for its cannibalistic mating process in actuality it only occurs 5-31% of the time. Especially in laboratory conditions of bright lights and confinement, the female is more likely to eat the male as means of survival. &quot;In nature, mating usually takes place under cover, so rather than leaning over the tank studying their every move, we left them alone and videotaped what happened. We were amazed at what we saw. Out of thirty matings, we didn't record one instance of cannibalism, and instead we saw an elaborate courtship display, with both sexes performing a ritual dance, stroking each other with their antennae before finally mating. It really was a lovely display&quot;. (7) There is one species, however, the Mantis religiosa, in which it is necessary that the head be removed for the mating to take effect properly. (5) Sexual cannibalism occurs most often if the female is hungry. But eating the head does causes the body to ejaculate faster. (3)

Anything that makes an individual less likely to reproduce will be selected against. Things that happen after reproduction do not affect the survival of the species and will not be subject to selective pressures.
References

E. M. Hull, J. W. Muschamp, S. Sato, Physiology &amp; Behavior 83 (2004) 291 – 307