First, note that the Timeline of the CHAP Links library does not support strings as Date, you should provided Dates or a timestamp with a Number (note that the successor of the Timeline,
vis.js, does support strings as date). Strings as Date work nowadays because most browsers now support creating dates from an ISO date string.
The issue you have is because you provide an ISO Date String without time zone information. Apparently not all browsers have the same default behavior in that case. Enter the following in a JavaScript console in both Firefox and an other browser:
new Date("2014-06-09T18:51:37").toISOString() // output is ambiguous, time zone information missing
and you will see them adding timezone information in different ways. To prevent these kind of ambiguities, you should provide timezone information yourself. To specify the time in UTC, add a Z to the end of the string:
new Date("2014-06-09T18:51:37Z").toISOString() // output is unambiguous