Yes, the 10 watts is divided between the two coils.  But since there ARE two coils being powered it means you add the power (5 watts being disappated in each) from both of the coils together and you get the same 10 watt total result as with a single coil.  There is no difference between one coil that adds up to 8 ohms and two coils each at 4 ohms that are hooked in series.  In simplest terms, an 8 ohm coil might be 1000 turns of fine wire that has a total resistance of 8 ohms.  To make a 4 ohm coil you just do 500 turns of fine wire (half the wire is half the resistance).  Now put two of those 4 ohm coils back to back and hook them in series and you have the original 1000 turn coil again.  That's what is going on when you wire the dual voice coil coil's in series to make the two 4 ohm coils into one 8 ohm coil.

There is also an explanation here

http://knowledge.sonicelectronix.com/car-audio-and-video/car-subwoofers/what-are-the-differences-between-single-and-dual-voice-coil-subwoofers.html

of the advantage of using dual voice coil speakers to provide the flexiblity of being able to get 2, 4, or 8 ohm ratings from the same speaker simply by wiring it differently.

Well so much for keeping things simple;

As you will notice in the link they are talking about “subwoofers” connected to an amp that is bridgeable, most likely 1 ohm stable. The purpose for that is to get two speakers into one location, so if you have room for 2 subwoofers you can run 2 dual voice coil woofers and drop your ohm load down to want ever your amp can handle.

But that is not what we are talking about here, the 6X9 in the link is a coil for the bass and a coil for the mid and a coil for the highs. The mid and high are on a shared line. Its apples to oranges.

Now the other problem is you are sending the full spectrum to the speaker, I don’t see any form of cap or coil to take the bass out of the tweeters and vice-versa. You make speakers play frequencies they are not designed to and it will sound like crap and in some cases it will distort and that will be hard on the amp in the radio. They can get away from it because we are talking about such low power that it will take many years to damage the amp.

That is a large magnet and there is a lot of mass in the cone, the woofer needs all 10 amps to play as it is designed. Notice it has 140 RMS watts max, generally you will run about 50 to 75% or full RMS, so its efficiency level is around 70 amps, got that in your radio?  

So your math is correct IF we are talking about 2 subwoofers of the same ohm and design, but the math does not work here. 

 From the linked web site

Banging head on desk.

Ok look at the photo. The large round part is the woofer, it takes up most of the space in the 6x9, the two round speakers in the center are the mid and high. The woofer is one coil and the mid and high are each one coil, the woofer is run off one input and the mid and high are on the other. A stock speaker does not have mid and highs built in, it is a true single 8 ohm coil speaker. What you listed is not the equivalent of a single voice coil 8 ohm factory replacement. What you listed is not two identical 4 ohm coils, if it were what then powers the mid and tweets? What is so wrong with using a single 8 ohm speaker that is designed for 10-15 watts? 

Why are you taking this so personal? You gave an option and so did I now let it go, OP can look at both and decide what works best for the needs. 

Yup, I am wrong, only been rebuilding speakers and custom mobile electronics since 85’. I really have lost interest in this but I will set the record straight and them you can just argue with yourself.

Photo 1:

 They are not tweeters, they are two mid speakers one is caped to block out lower frequencies. The cap is the round black piece on the left. The way this speaker is set up the woofer plays all frequencies, from around 50 HZ to its distortion point, probably around 500 HZ, it should be choked at 80-100 HZ but that is a design defect of that speaker.  The mid cuts in at about 80 HZ and goes to 20K or so. The only good thing about this design is the other caped mid can’t play the lower frequencies. So you will get OK sound out of what the radio can produce.

Photo 2:

That is the dumbest thing I have ever seen, why on earth would you bolt a metal plate to a speaker magnet. That mount is affecting speaker efficiency, You never want something metal on the back of the speaker magnet.  However the red is going to mids and high as I have said, green is going to woofer as I have said.

Rest of the photos:

I am not talking about how the speaker is wired internally, I am talking about how it is wired to the radio in this photo on the web site you linked to:

So you have one output on the radio, either positive and negative or negative to ground.  In the photo it is wired in series, 2 coils at 4 ohms to get 8 ohms, at the very start I said it will work but it will not be efficient and it will be hard on the radio. That speaker wants 70 watts to be efficient, the radio can’t do that.    Now you can run it in parallel and that would solve the shared watts problem, but you will over drive the amplifier in the radio because the ohm load will be 2 ohm and that will cause the amp to run at 100 watts for a split second before it smokes. The fact is this design has no ballance. 

Now if you have a head unit with a front and rear output you could hook one front and rear to each side but it would sound strange on some songs. But if you hook up that speaker as shown you will need higher volume to get the same sound as a single voice coil.

Now if you were going to run one of the dual speakers at the bottom of the page like this one:

Then you will have two identical 4 ohm speakers, that would be in balance, it will still effect watts but it is closer to what you are trying to say.

And again why does he have to do it your way? Why can’t he just get an 8 ohm singe voice coil speaker? We have installed turn switch products, they are very good and the price is about the same and there are lots of other companies that do the same thing. So why can’t he just use a single 8 ohm?  

Look, it’s clear you are happy with your set up, not everyone does things the same way, just stop talking about things that you have no knowledge in. as for OP, if you need more info send me an email or PM I am happy to help, but this is not productive.