It's likely impossible to determine why premiums are increasing in a meaningful way; not only is the interrelationship between the various data points very complex, but some of the increases are likely due to decisions by people who do not and will not publicly post what they decided and why.
However, it is possible to compare health insurance premium increases over time to see if the increases in employer-sponsored health insurance premiums are comparable or not to the pre-ACA timeframe.
Since the ACA phased in over a few years, we can compare the period 2008-2010 "pre-ACA" and 2013-2015 "post-ACA", ignoring 2011-2012 as being unclearly affected by the ACA phase-in. For this, I will look at single coverage premiums only for the purpose of simplifying the analysis.
I found a good table of 2008-2010 premiums from the NCSL; they list the following:
Kaiser Permanente had a good list for 2013-2015 here:
From 2008-2010, the average growth was around 6% per year. From 2013-2015, the growth averaged about 3%. In both of these cases we are comparing total premiums (sum of employer and employee contributions).
So, from a data-driven look, it seems that the premium growth is lower post-ACA than pre-ACA, so it's unlikely that the ACA could be accused of causing increased premium growth. Of course, this is US-wide average, and on a state-by-state basis there may well be significant differences that may or may not be related to the ACA.
One thing that is covered on the NCSL page linked above that is interesting: while the premium growth has slowed significantly (about 50% of the growth pre-ACA), health insurance premiums are a higher proportion of employee's wages, and that growth is continuing - because wage growth has not kept pace with inflation post-2008 recession. Employee contributions also may be higher post-recession; many companies reduced their contribution percentage (as my then employer did, for example).
Finally, increases in the ACA plans are also commonly overstated. They largely are in line with employer plans or even less.
In 2015, premiums were basically flat, decreasing slightly in fact - see the KFF analysis here. 2016 saw a 3.6% by this methodology (see the 2016 analysis).
It's very easy to cherrypick examples that are favorable to any interpretation from the data, though; there are such big swings as a result of the different conditions in the marketplaces that it's easy to pick a few that have high swings and claim the ACA has massive premium increases, or pick a few that have low swings and claim it's reducing costs.