They definitely have to know if there is a reciprocity law regarding that other state ... :-) ...
And Oklahoma takes care of the law by the issuing of the concealed carry permit. So, to the officer in the other state (whatever that state is) ... they would first know whether there is reciprocity with that other state, and then they would see if they actually have a permit with that other state,
And you still HAVE TO ABIDE BY THE LAWS OF THE STATE YOU ARE IN ... no matter if you have a permit from your home state,
For example, Oklahoma only allows people to open carry by permit only. But, if you do have that permit in Oklahoma, you may NOT be allowed to open carry in that other state, even though you have the permit in Oklahoma to do so. You may ONLY be allowed to carry concealed,
SO YES ... you have to abide by the law of your home state ... AND ... the laws of the state you are in, when it comes to these things.
Here’s a reciprocity map for the various states ...
http://www.usacarry.com/concealed_carry_permit_reciprocity_maps.html
/johnny