There are two railway stations in Kutaisi, but we mean this nearer the city centre (Kutaisi I Railway). The second is freight station.Google Map
Let's take for example the train Tbilisi-Kutaisi. Look below:
According to the schedule the train leaves from Tbilisi at 9:00 and arrives to Kutaisi at 14:30 (headers of columns "Departure" and "Arrival"). The next two columns have the same headers "Departure" and "Arrival", but this time the direction is inverted: Kutaisi-Tbilisi.
So, this time the train leaves at 12:15 from Kutaisi to Tbilisi, where arrives at 17:15.
Why is it so strange? I don't know, but it is. Most likely it's about wrong translation the headers (look below).