For those people who's job requires them to be armed (private security, armored car drivers), this is excluding government employees, are they allowed to carry off the job?

I don't believe so, only while they are performing official duties.

I have also heard that they aren't even supposed to use it according to company rules. It's all heresay though.

There's nothing I can find in HRS 134 that says anything about "except when required by employment."  If you have a license to carry, I believe you have a license to carry.

However, never having seen a Hawaii license to carry, I don't know for a fact that there isn't restrictive language on the license.  I do know that there have been instances in the news over years past involving HPD officers who were off-duty, carrying, and responsible for doing something good. 

HRS 134-9 notes that "Where the urgency or the need has been sufficiently indicated, the respective chief of police may grant to an applicant of good moral character who is a citizen of the United States of the age of twenty-one years or more, is engaged in the protection of life and property, and is not prohibited under section 134-7 from the ownership or possession of a firearm, a license to carry a pistol or revolver and ammunition therefor unconcealed on the person within the county where the license is granted." But, no mention of restricting said open carry to times of actual work. However, HRS 134-11 does mention some restrictions on when someone can carry concealed, but it applies to Federal or State employees, or their subdivisions. But nothing for open carry....at least that I could find.

§134-11  Exemptions.  (a)  Sections 134-7 to 134-9 and 134-21 to 134-27, except section 134-7(f), shall not apply:

     (1)  To state and county law enforcement officers; provided that such persons are not convicted of an offense involving abuse of a family or household member under section 709-906;

     (2)  To members of the armed forces of the State and of the United States and mail carriers while in the performance of their respective duties if those duties require them to be armed;

     (3)  To regularly enrolled members of any organization duly authorized to purchase or receive the weapons from the United States or from the State; provided the members are either at, or going to or from, their places of assembly or target practice;

     (4)  To persons employed by the State, or subdivisions thereof, or the United States while in the performance of their respective duties or while going to and from their respective places of duty if those duties require them to be armed;

     (5)  To aliens employed by the State, or subdivisions thereof, or the United States while in the performance of their respective duties or while going to and from their respective places of duty if those duties require them to be armed; and

     (6)  To police officers on official assignment in Hawaii from any state which by compact permits police officers from Hawaii while on official assignment in that state to carry firearms without registration.  The governor of the State or the governor's duly authorized representative may enter into compacts with other states to carry out this paragraph.

     (b)  Sections 134-2 and 134-3 shall not apply to such firearms or ammunition that are a part of the official equipment of any federal agency.