Alchemist5,
When dimethylacetamide is heated with water over a length of time usually taken by most published methods a reaction takes place and methylamine(?) and dimethylamine(?) are formed and possibly other artifacts or impurities in the DMA are seen to elute.
Other reactions can take place depending upon the matrix and other factors.
This methylamine peak elutes early, often near methanol on many columns.
The peak near DMA is DMF or MMA and should elute just before DMA, this MMA is a normal small impurity found in most lots of DMA.
What can happen?  If your flow path is reactive rather than inert (this is all relatively speaking now) the MeAmine or DiMeAmine can be absorbed rather than elute as a distinct peak.  A well used system will often not elute the peak although other alcohols, ketones, amides, etc will elute without a noticeable problem.
The HCl you added makes an amine salt of the MeAmine or diMeAmine and inhibits its volatility so it never get to the flow path or at least is suppressed in concentration.
BTW, I found that if one uses smaller samples the LOD for most analytes does DOWN, not up, which is counterintuitive, but true.  I never use more than 100µL of dissolved sample to do headspace analysis and am able to achieve a reproducible equilibrium for most residual solvents in 6 minutes of heating.  Alcohols like i-BuOH or IPA will take 8 to 10 minutes to equilibrate to a near maximum level.  This greatly reduces the artifacts that can be formed.
If you read my short two page HS article published in the Journal of Analytical Chemistry in 1997 you will see that I stated there:
"The dimethylacetamide produces artifactual peaks which coelute with methanol and dichloromethane and are adjacent to hexane, isobutanol, and dioxane. "
I only heated my samples for 6 minutes and was able to see and separate 1ppm of 18 residual solvents (including dioxane) using only 1mg of sample dissolved into 25µL of water (with a small amount of DMA).
I used the Tekmar 7000 modified with fused silica coated components, of which I was a beta tester.
Oh, for the good old days.....................    
 
best wishes,
Rod