We do not use Douglas barrels sorry.

Quoted: A quick search on Brownell's website shows that Douglas makes only 1/9 and 1/14 twists for .224,

Brownells does NOT list the full line of douglas barrel blanks.
Heck, even the Douglas website does not.
I just received a couple stainless steel 1:8 twist blanks last week from Douglas that I have available for 300x221 builds.
No mention of 1:8 twist 30 caliber blanks even being available.
You have to call and ask and they will probably make you about anything you could want.

I do use a lot of Douglas and Shilen blanks in the barrels I build.

I email the builder and he replied that it is the same barrel (??) and that he could get it faster by ordering from DMPS than directly from Douglas.

The DPMS barrel blank is likely from a company like Green Mountain, ER Shaw or Wilson.
None of these companies make a barrel that's even near the quality of a Douglas XX grade barrel.
I know, I have looked down and used blanks from all these companies.
Douglas is the Good Stuff.

I'm also not sure that Douglas sells profiled AR barrels, so your smith would have to have made the barrel from scratch.
That's a lot more work than just ordering a finished barrel.
He's being lazy.
Telling you that the barrel from DPMS is the same as the one from Douglas is PURE B.S.
Call his bluff.

I am a custom barrel and upper builder.
Sounds like the guy you were dealing with is an assembler.
There's a big difference from someone that can take a raw barrel blank, chamber and profile it, set headspace at any specific dimension you want, chamber the barrel in such a way that the throat is perfectly centered for optimum accuracy etc...
Assemblers just buy parts and put them together.
They have no control over the internal workings of the barrel.
The internals of the barrel are the MAIN place that accuracy lives and dies in the AR-15.