Does animal tranquilizer really work as fast as we see on Dexter?

TL;DR;

• All sedatives take at least 1 to 2 minutes before taking effect; hence, the immediate passing out seen often in Dexter is unrealistic. The biggest hindrance to opioids is BBB.
• Dexter uses a tranquilizer so potent that it will just kill the victim. Aww, there goes the speech.
• I can't recall any episodes with a different 'attacking spot' than the neck vein (jugular vein), but an abrupt insertion of the needle in an unstable subject is most probably IM injection, and thus, acting even slower.

It seems that use of chloroform in fiction to sedate patients goes back so long it was a widely known phenomenon in 1864. You could argue it's one of the most tired clichés of all time. In fact, the whole idea of sedatives/tranquilizers/anesthetic drugs acting instantly — i.e., in a matter of few seconds — is ridiculous. Inception dodges this by showing us that there's some passage of time not being covered on the screen by a deliberate breaking of the flow of events, and it could be a matter of seconds, or minutes for a member of the team to go unconscious.

As far as I'm concerned, there are numerous anesthetic drugs and tranquilizers which belong to a vast group of different chemicals, and their scopes are tangled within each other, with anesthesia being more focused on the individuals' well-being than tranquilizing (as the word usage usually implies). More people would be familiar with the former if they've undergone some form of surgery, and they can confirm that you would first feel drowsy, then too heavy to 'move a muscle', and then the next thing you see is rehabilitating on a bed. Point being, that it is not instant. In fact, that's perhaps the only thing that's invariably consistent among tranquilizers.

The police don't use tranquilizers for good reason. It's way too easy to miss the mark of the right dosage, either providing insufficient dosage, resulting in a still-conscious but slightly drowsy subject marching forward with a lethal weapon, or overdosing the subject, which usually kills them.

Dexter uses a tranquilizer named etorphine, notable for its potency. Realistically, the subject would wobble back and forth before dropping to the ground after a good 1–3 minutes, and then most probably die of overdose. It's an opioid used for elephants and rhinos, but that doesn't mean it'd act faster on humans. It just means its LD50 is ridiculously, dangerously low.

Passing out is not instant, even for this chemical, notable for its fast action. This study analyzed the symptoms of the drug in mice, rats, dogs, and a few other species. One notable quote would be

The predominant effect of etorphine given parenterally to dogs was the rapid development of catatonia associated with total analgesia. Thus the effects of the drug in nine animals, seen within 2 min of intravenous injection of 2–5 ?g/kg and lasting 30 min–2 hr. were ataxia and miosis followed by deep narcosis during which surgical procedures could be performed.
_{Catatonia: Lack of movement and communication
Analgesia: Inability to feel pain
You can safely ignore the rest of the jargon. Emphasis mine}

Also check out this page, which serves as a compilation of bad things that happens to people in touch with such a potent opioid.

To answer your question on the difference between an injection in the neck, and an injection in the hand, there are several types of injection, the most common being:

• intravenous (IV) (the fluid being inserted right into a vein): Very fast, as the circulatory system in directly involved.
• intramuscular (IM) (the fluid being inserted into a muscle): The drug is absorbed by the blood vessels, slower
• subcutaneous (the fluid is injected barely under the skin): Slowest absorbance, just not enough blood to 'go around'. My point is, access to the circulatory system is the limiting factor here.

A prepared strike means Dexter can go for the central vein (referred to veins that are in torso and often close to the heart), but basilic vein is also commonly used for IV injections. There is more blood flow on a bigger vein, but I doubt that, if it is indeed IV injection, there will be a significantly different result, since blood circulation to vital organs is pretty fast, and the biggest blockage to etorphine, or any sedative, is blood–brain barrier.

I haven't seen the episode you're referring to (I've only been sporadically watching the show), but aiming for the arm/hand of a subject that is not immobile almost certainly means it's going to be an IM injection, and that's typically slower than IV, and your suspicions would most probably be correct. I can tell it would almost certainly be IM since it's actually pretty hard to inject even huge, visible veins, as is evident from all the poor patients whose veins collapse after numerous injections, by trained professionals.