NOAA has a detailed write-up and explanation on what occurred during the afternoon hours, along with an eyewitness account to the event. Part of that excerpt is listed below from Brian Coen, who observed the sea level change at Barnegat Inlet.
Around 3:30pm on Thursday June 13, 2013, Brian Coen was spear fishing near the mouth of Barnegat Inlet; just south of the submerged northern breakwater. Earlier in the day around noon, thunderstorms had moved through the area. By 3:30pm the weather was overcast with a light east wind. At approximately 3:30, the outgoing tide was amplified by strong currents which carried divers over the submerged breakwater (normally 3-4 feet deep). This strong outrush continued for 1-2 minutes and eventually the rocks in the submerged breakwater were exposed. Brian backed his boat out before being sucked over as well.
At this point, Brian noticed a large wave coming in, approximately 6 feet peak-to-trough and spanning across the inlet. The upper 2 feet of the wave was breaking. This wave occurred in conjunction with a reversal of the current such that even though the tide was going out, a strong surge was entering the inlet. This surge carried the divers back over the submerged reef and into the inlet from where they were picked up. On the south jetty three people were swept off the rocks which were 5 to 6 feet above sea level at the time. At least two were injured requiring medical treatment. There was no more strong activity after about 5 minutes.
The tidal gauge at Lewes, DE, had a 12 centimeter (about five inch) spike in peak amplitude, which you can see outlined on the chart below. The spike occurred between 3 and 4 PM, about five hours after the line of storms crossed off the Delaware coastline.
NOAA researchers also speculate that slumping along the continental shelf (where the ocean floor drops off quickly to several thousand feet below sea level from only dozens of feet) may have played a role in the generation of the mini-tsunami but the timing of the derecho/squall line is such that weather is at least being looked at as a possible factor.
These sea level changes are nowhere near the levels observed in larger earthquakes, such as the one that struck Japan in 2011 or Indonesia in 2004. However, it is a bit unique for this part of the world.