Why does the time differ by 4 hours on certain apps? In Yosemite I have my timezone explicitly set to GMT-5:00, and in the tool bar the clock shows the correct time. Several apps, including Mail, also show the correct time.

However, I've noticed that some apps show the time as if it were 4 hours ahead. Slack for example, as well as Facebook's web-based chat. 

I have no idea as to what could be causing this. Any help would be great!
Since you have system time set up correctly, then I guess the problem is within the apps you named. Most probably, they setup their internal time based on location of the proxy you might be using and which is located somewhere in a TZ 4 hours ahead.