Please excuse if this has been discussed in an earlier thread.
Delta EST / GMT should always be -5. Problem exists with EDT and other time zones with countries using Daylight Savings times.
I'm looking at the chan post by anonymous in your graphic for this analysis.
Europe/England went from Central European Summer Time/British Summer Time to Central European Time/Greenwich Mean Time at 2AM on Sunday, Oct 29 2017.
US changed on one week later, November 5.
That would mean at a 2AM on Sunday, Oct. 29, CEST/BST ends and goes back one hour (to CET/GMT). Thus, 23:15 BST in England returns to 22:15 GMT.
For one week, DC/US would stay at 18:15 EDT. IOW, delta EDT/GMT = 4hrs for that week.
Doesn't answer, though, since the anonymous post in graphic is Oct. 28, why that issue would appear before the time change actually goes into affect, Which is 2AM on OCT 29, 2017.
Unless the device (in the anonymous post presented in the graphic) used to make the tweets was in (or set for) a time zone = or +3hours GMT, which would then account for a 4 hour difference?
Notice the blue outlined timestamp has a time of 15:08:48-04, which is 3 hours before 4chan time of 18:15.
So, if chan time = GMT (not sure here), maybe post was made in GMT +3 timezone (Eastern Africa + Eastern Mid-East) countries.
Many in this timezone don't use DST, anyway, so hour at which BST/GMT WRT EDT changes is moot.
So, in the rare case my thinking isn't fucked up, this anonymous chan poster could have been military/civilian assigned/TDY to AFG/Iraq/SA/Turkey.
Time Zones are important, so I think all aspects have to be considered in coordinating chan and Twatter posts.