The source they list is a recent report from the New England Journal of Medicine. The 10.3M number is given there, but there are a few other factors to consider.
Your main concern seems to be about the historical trend. They say this about that:
As compared with the baseline trend, the uninsured rate declined by
5.2 percentage points by the second quarter of 2014, a 26% relative decline from the 2012–2013 period. Combined with 2014 Census estimates
of 198 million adults 18 to 64 years of age,19 this corresponds to
10.3 million adults gaining coverage, although depending on the model and confidence intervals, our sensitivity analyses imply a wide range
from 7.3 to 17.2 million adults.
This doesn't clearly say what time period/method they use to get the "baseline trend", so it's hard to give a precise figure, but it's clear that they're adjusting for some sort of previous trend.
They also note that the major gains were in demographics consistent with the predicted effects of the law:
The pattern of coverage gains was consistent with the effects of the
ACA, with major gains for persons likely to be eligible for expanded
Medicaid on the basis of their income and state of residence but
smaller and nonsignificant changes for low-income adults in states
without Medicaid expansion.
...
Absolute gains were largest among young adults and Hispanics, two
groups with high uninsured rates at baseline. State-level estimates of
coverage gains were significantly associated with official HHS
enrollment statistics, showing that each percentage point of the state
population enrolling via the marketplaces was associated with a
half-point decline in the uninsured rate.
However, they are careful to point out that the study is not perfect, and in the discussion section they talk about limiting factors, such as:
Nonetheless, the inherent lack of a control group precludes a causal
interpretation for these findings, and other unmeasured factors may
have contributed to these changes.
In summary, it looks like HuffPo did what most journalists do: Take a single number/soundbite from a paper and report it. There are confounding factors, and the number quoted is jut an estimate, but it's clear they have taken a lot into consideration. It's not just a WAG.
