please help me decide between these three road bikes..

I would buy the Madone and get a good fit. The 105 is definitely a better group set and you will adapt to the Madone frame nicely.

Madone for sure. Unless you are riding Roubaix you don't need a domane.

Have you been fit?

If not do that first.

Have you gone to other shops?

If not do that as well to learn and get other ideas and see other bikes.

Sounds like someone in the shop has pushed you in one direction. Frequently new triathletes go to a bike shop and they get sort of evaluated by the staff and pushed in a certain direction what type of bike would be best for them when their assumptions are off. Some of the stuff I have heard bike shops tell new triathletes is horrible advice. All to often new triathletes buy a bike only to have bike regret and end up buying a second bike within a year due to bad bike advice from the shop they trust. Bike shop employees often don't know  much but pretend to know a lot about triathlons.

What are your goals in riding?

Do you want to be fast? do group rides? do tris? do bike racing? social riding? What?

This year's Tiagra is last year's 105. Seriously. It's decent stuff, and you can (and will) eventually trade up when things wear out. The frame? Not so much. I like the idea of the Domane for long distance comfort. Assuming it fits, that's the way I'd go.

That isn't exactly true, some of the technology "trickles down" but there are still some serious differences between groupos.

I would not go back to Tiagra on a bet. My first bike had Tiagra, it works but not very well. My current roadie has 105 on it and I am happy with that. My tri bike has Ultegra. Would have preferred Ultegra on the Roadie but the bike was the right price so I went for it. 105 is the lowest I would go on components. 

Your situation is different than what most of us assumed. Clearly you are a solid cyclist and getting another bike to add to your stable.

I would suggest riding the two you like best on roads similar to what you ride and go from there. Will your shop allow you take them out for a 1-2 hour ride to see which is right for you.

I can say a little something about the move to SRAM.  My most recent roadie has SRAM Rival. I wanted to try something different.  I am not a huge fan of the double-tap shifting and would go back to Shimano on the next bike.  I can't explain exactly why, but when I ride my old roadie with crappy components I feel like shifting is "easier." 

Just my $.02

I thought that maybe 2013 Tiagra was very similar to 2012 105 now that it's 10 speed, but many people agreed that it's not up to par...yet.

As for the person that claimed simply swapping out the rear derailleur to 105 would be a simple fix...I disagree.  It would help a little, but you would still be limited largely by the Tiagra shifters.