The proper way to tune a djembe is tabletop tight, until the head is starting to choke.   Let's put it this way.   Rules for a real (African) djembe:

1.  Way too loose-Djembe is dead sounding, no matter how you play it.   You can push the head in easily in the middle.

2.  Tighter-Now it starts to sound like a djembe.  Big full bass note,  good tones and slaps, but there is some ring, like a snare drum.  If you're real paranoid about the head breaking, stop here.   Head pushes in just a bit in the middle.

3. Pro tuning-Tabletop tight.  If you push in the middle of the head, it almost doesn't give.  Remember that snare drum like ring?   Keep tightening until the ring starts to go away.  You actually want the head to be choked, tightened past the sweet spot for resonance.   Now,  your tones and slaps should be crisp and cutting.   The bass response may suffer some, because the head is so tight.

Don't be too paranoid about the head being tight, especially if you have a mid/high quality djembe.  The head will take it for a long time, if you observe a couple of rules.  

Rule one-With a well tightened djembe, avoid  super hot enviroments like the plague.   Don't even think of leaving it in the car on a hot day, or in any similiarly hot enviroment.  If you must leave it in a very hot place, detune it so the head won't split.  Try to avoid getting the head damp.   Cold may cause it to detune a tad, but it will retighten itself when it warms up.  Djembe heads are so tight that this usually isn't a real problem.

Rule two-If you hit it with a stick, do so very lightly with a small, light stick.  You're best off just using your hands.

Rules for a Remo djembe-You won't have to worry so much about temperature/weather.  You can leave it in the car.   You can hit it with a drumstick, but I wouldn't advise rim shots.  Your head is a Mylar Fiberskyn head, the same as the ones used on drumsets, except for the shape.  The Mylar head will ring a lot.  I muffle it with a small, one inch square of cloth, placed an inch or so in from the downhill edge of the head.  I put tape only on the uphill side of the piece of cloth, so it can move freely against the head.  This increases the muffling effect a lot.  I would tighten a Remo up until the bass note is just starting to suffer.  Once again, tight is right.  You want those crisp, cutting tones and slaps.  Tighten slowly and evenly, like you would with any drumhead, if it's key tuned.  If it's rope tuned, just keep pulling diamonds until you get to where you want it.  Because the head is Mylar, you won't have to retune much or very often.  The main disadvantage of a Remo is that they just don't sound quite like the real thing, no matter what you do.  If you get serious, you'll want the real thing, but the Remo is a good place to start, and a good drum to have if you're not that serious about it.

Marker's tuning suggestions are spot on. By keeping the head tight (ie table top), the slaps are effortless; the drum practically plays itself. The concept is very similar with any hand drum where slap tones are used ... such as the "macho" side of the bongos, as well as the quinto (solo drum / smaller conga).

The moon gel thing works well ... but you can remove the ring you are talking about ... just by tuning the drum a little differently. Traditionally speaking, that ring is wanted for projection in the ensemble; but it's a controlled ring via tuning. The low-end is not as big with this tight tuning, but again, that's what's called for in a traditional ensemble because the djun-djun are covering the low-end. If the djembe were to have a lot of low-end, they instruments would clash.

Feel free to tune the drum to fit your musical situation. If I'm not using my djembe in a "traditional" fashion, I often have it tuned to get a fuller sound in the low-end ... and yet still have a nice slap and open tone.

Moon Gel works well, but you'll need to experiment to find the exact that works best for the sound you desire.

Well, one thing about a Remo:  They're nearly waterproof.

Actually, I recently tried to retune my Remo really, really, tight.  The ringing actually got worse.  I ended up detuning it back down to somewhere between djembe and conga territory, where the ring is easier to control.

My main squeeze Arfrican djembe continues to deliver crisp, cutting tones and slaps, with decent bass.

The difference between a real djembe and a Remo is kind of like the difference between a tube guitar amp and a transistor guitar amp.

The transistor guitar amp is usually cheaper for what you get, has more tits and whistles, is more reliable, and lighter and easier to carry.

A tube guitar amp is more expensive,  less reliable,  requires maintenance and expert repair work to keep it operating at optimum.

So, why do most guitar players use tube amps?

 It's the sound.

That's  the same reason people prefer real djembes over Remo's or other imitations.