First of all, assuming the deists are someone "whose logic is different" than the atheists, that right there is something that could be argued. Further, you and I can reach two different results with the same logic if we have different premises; it doesn't mean that two people who do not agree on something are using different types of logic. If that were the case, then there would be seven billion different logical systems.
Secondly, because of the thing I explained, you cannot build an analogy between two different languages and two different ideas.
And to your second question, what makes logic and reason right is that it is "Consistent and Complete". And do not make the mistake to think that "logic is a science". That would make logic falsifiable. However logic is not a science, it is composed of the definitions. Logic and reason is right just like you cannot prove x=3 after you defined x=2. What I mean is, if you know that x is a natural number, and you say "Ouw, then x is 2", then what you said is falsifiable. However if you say that "Let x be 2", then you say "Ouw, then x is 2", there is nothing false here, because you defined x that way. You could have define x as "Let x be 3", and say "Ouw, then x is 3", and that would be true too. It's just about how you define it. Logic is a definition; whateverdefinition. Everything that you definedefined is right because you defined, it is defined that way.