Does an employer have to pay for travel expenses from one job site to the next? Should a employer advise that traveling is a part of the job?

As a legal question, an employer isn't automatically responsible for these expenses, although it often makes good business sense.

If the employee is paid by the hour (or is legally entitled to overtime if worked, even on salary), then all of the time spent on travel between job sites is work time that has to be paid for in full.  The employee should also keep detailed, daily records of the travel costs between job sites, because unlike commuting, these costs are deductible from income for tax purposes.  With an older car, the IRS mileage rate can actually end up "making" a little money for you this way.