The answer is no, they do not need to be wearing their work clothes. just like a LEO does not need to wear his work clothes to and from work.
In fact, it is a good idea NOT to wear the uniform when not working.
LEO have no requirement to be wearing 'work clothes' while carrying, but 'security guards' most certainly do if they are carrying loaded.
PC 12031. (a) (1)
A person is guilty of carrying a loaded firearm ...
...
(d)
Subdivision (a) shall not apply to any of the following who
have been issued a certificate pursuant to Section 12033.
...
(5)
Uniformed security guards, regularly employed and compensated
in that capacity by persons engaged in any lawful business, and
uniformed alarm agents employed by an alarm company operator, while
actually engaged in protecting and preserving the property of their
employers or
on duty or en route to or from their residences or their
places of employment, and security guards and alarm agents en route
to or from their residences
or employer-required range training.
Nothing in this paragraph shall be construed to prohibit cities and
counties from enacting ordinances requiring alarm agents to register
their names.
12033. The Department of Consumer Affairs may issue a certificate
to any person referred to in subdivision (d) of Section 12031, upon
notification by the school where the course was completed, that the
person has successfully completed a course in the carrying and use of
firearms and a course of training in the exercise of the powers of
arrest which meet the standards prescribed by the department pursuant
to Section 7583.5 of the Business and Professions Code.
[In essence Guard-Card holder]
Additinally - I think there are specific 'marking' requirements for the uniforms as well, but I'm not certain.