This will probably work
The spell text is quite unambiguous about the knowledge acquired by the caster (PHB p. 289, bold added):
Until the spell ends, a creature
who enters the spell area for the first time in a turn or begins his turn, must make a Charisma save throw … You know if each creature succeeds or fails in its throw of salvation.
Now, as DM, you could declare that this knowledge depends on the awareness of the existence of a creature, but that would add restrictions that are not present in the current spell. As it is written, it seems that every time a creature on the radio succeeds or fails against this salvation, the caster knows.
Why is this balanced?
Honestly, a second level spell should reveal the presence of invisible creatures. After all, they already do. The spell See invisibility (2nd level) not only reveals that an invisible creature is present but also lets you see it. And the first level spell Alarm it will allow you to detect when any (invisible) creature enters a restricted space for 8 hours, not just 10 minutes (and it is a ritual, so it could be launched without spending resources but time).
Keep in mind that invisible creatures are not always undetectable by default. An invisible creature usually makes enough noise for everyone to know where it is, unless it tries to hide. Therefore, the passive perception of your group may also be sufficient to reveal the presence of invisible creatures (although they will remain invisible).
All this is to say that your players realizing that Zone of Truth could reveal hidden creatures is not as unbalanced as it might initially seem. That said, I had more specific questions on how to answer this tactic:
What could you do about it?
There are many options, but some jump.
- Make the spell reveal invisible but benign creatures.
As I read it, this spell will allow the characters to know about invisible enemies, but also about other creatures. You could tell your players that something has failed in a saving throw, but no other information. If everyone proceeds to attack him, they can determine that they have passed a round in combat by killing a Sprite that goes through the dungeon over their own business.
- Make enemies go through the Zone of Truth
The description of Zone of Truth is not clear about whether the area itself is visible or not. If you declare that it is visible, creatures that try to avoid detection can simply move around it (if possible). Even if you decided that the spherical zone of truth was invisible, creatures could quickly determine where it is because …
- The spell reveals both the casters and the targets.
Note that according to the text of Truth Zone (ibid).
An affected creature is aware of the spell. and so you can avoid answering questions that you would normally answer with a lie.
As such, every time an enemy enters the Zone of Truth, he will realize that someone has cast that spell there (if the save throw fails). They might not know that the PCs were in the area before, but now they certainly are. Then the spell essentially gives as much as is needed in this regard.
- Make enemies run through the area
Note that Truth Zone will not reveal where The invisible enemies are exactly: only that they are somewhere in the area of effect of the spell when they fail or succeed in the saving throw (credit to Medix2 for pointing this out). Enemies could enter the zone of truth, then simply leave it. The PCs would know how many invisible enemies are present, but they would not know where they are. In many situations, this would give invisible enemies most of the same advantages they had before (minus the possibility of surprising their enemies).
On a personal note, I want to add that none of those tactics are my favorites. I would suggest the latter as an alternative.
- Let this tactic work.
This is a creative and intelligent use of this spell that thinks outside the box. Such an idea must be rewarded. If your players want to dedicate resources to protect themselves from invisible enemies, this is a viable way to do it (and provides the benefit of only a lower level spell, Alarm, and for less time).
If you want this tactic to fail, I suggest that there is some compelling reason to do so (like the enemy they are fighting with is intimately familiar with the way they operate).