Yes, that is definitely the problem, that the form values are as strings, which means you are performing a string comparison.
You can deal with that by turning the strings in to numbers.
One way of doing that is with the parseInt() function, but that can get messy when you're always putting in the radix number too.
var number = parseInt(string, 10)
So, a preferred way is to use Number() instead, which casts the value to a number.
var number = Number(string)
I'm extracted out the form reference to a separate variable, to help simplify your code, which results in this for the appropriate part of your jsfiddle code:
var form = document.forms.timesheet_office1,
arrival_customer_hrs = Number(form.time_arrival_customer_hrs.value),
arrival_customer_min = Number(form.time_arrival_customer_min.value),
departure_customer_hrs = Number(form.time_departure_customer_hrs.value),
departure_customer_min = Number(form.time_departure_customer_min.value);