Mechanically, Truth zone is almost foolproof for loyalty testing
As you say, any attempt to resist or avoid the effects of Truth zone alert the launcher. And in the context of a loyalty test, avoiding the effect is synonymous with admitting disloyalty. To my knowledge, there is no way to avoid the effect of the spell without alerting the caster that you did it. So, if you want to pass the loyalty test, you will have to do it by saying what your character thinks is the truth.
Believe your lies
However, this leaves at least a small loophole difficult to exploit: Truth zone only prevents a creature from speaking a deliberate lie. If you manage to believe your lies, you will be able to say them while having the effect of Truth zone. For example, if the question of loyalty is something like "Are you loyal to the Empire?", Then you will be able to answer with a simple "yes," even if you plan to murder the person. Emperor, as long as you wish. really and honestly believed it would help the Empire. Obviously, it's a very circumventing the situation, but I want to emphasize that this is materially different from being evasive or "lying with the truth".
In practice, when you try to use this, you should probably expect reactions from your DM, asking you if your character really believe that. This "loophole" has a concentration on character rather than mechanics. Therefore, if you plan to do so, be prepared with a solid story to justify your honesty. And of course, be prepared to accept the fact that a slightly different question might reveal that your interpretation of loyalty differs from that of your interrogators. In the example above, you would not go well if you were asked instead "Are you loyal to the emperor?"
Unfortunately, I have no experience to share about using this "loophole" in a real game. I simply emphasize that this is the only loophole I can think of.