SetDirectory[NotebookDirectory[]];
data=Import["2016-04-20_06_15_12.107020_365nm.txt","Data"];
(*CHANGE 2016-04-20_06_15_12.107020_365nm.txt to your filename. Files must be in the same folder as this notebook*)

AbsoluteTime[data[[1,1]]]

dataToPlot={(AbsoluteTime[#[[1]]]-AbsoluteTime[data[[1,1]]])/60,#[[2]]}&/@data; (*This converts the time to minutes and scales it to start at 0*)

ListPlot[dataToPlot]

dataToFit=Select[dataToPlot,1.5<#[[1]]<2.5&]; (*Change this time interval (1.5,2.5) to reflect the initial linear range in your data*)

(*Fit a line to dataToFit to determine the rate - See tut 2 and 3*)