As one or more other pointed out, and regarding the specific circumstances, there's nothing wrong with the cat cop showing on his own time, and in civies.
You know who he is. You invited him there and made clear you don't want the kitties suffering 20 hours in a trap. So expecting him to dress up for the job in his off hours would be unreasonable. Complaining about it might compromise his desire to go the extra mile for you.
All that said, your cat ranch, your rules. He'd have no authority to be on your property absent permission from you.
In the end, it sounds like he is going an extra mile, as are you. Accordingly, if both of you are inclined to be a bit gruff, you'd both do well to figure out a get around, which starts with laying out ground rules (he gets some too).
In the end, he doesn't have to show up at all, unless he says he will (Public Duty Doctrine even applies in this situation).
As to garb, he's a cat cop anytime he's performing cat cop duties.
Inasmuch as he is a public official with the power to issue citations, he is bound by certain laws. For example, if you pulled all HIS traps, gave them back to him, and informed him he was no longer needed, or would only be called on a situational basis, he cannot step onto your property, aside from the walkway to deliver service, mail, UPS and so on. Anything more violates state and federal constitutions.
Now to the three cat rule:
(1) It's on the state / county / city /town to prove you have forty-seven and 3/8ths cats, rather than you to prove you don't.
(2) People talk too much. You, likely, already told the guy too much, or, otherwise, let him know too much. However, his memory can be ripped apart in the course of the administrative processes, or the judicial witness stand. After all, he misunderstood what you said. "Right"?
(3) Making threats or demanding money not owed is a crime:
18 USC § 1961 Definitions
As used in this chapter -
● (1) "racketeering activity" means (A) any act or threat involving murder, kidnaping, gambling, arson, robbery, bribery, extortion, . . . , which is chargeable under State law and punishable by imprisonment for more than one year; (B) any act which is indictable under any of the following provisions of title 18, United States Code: . . . , section 1341 (relating to mail fraud), section 1343 (relating to wire fraud), . . . , section 1503 (relating to obstruction of justice), section 1510 (relating to obstruction of criminal investigations), section 1511 (relating to the obstruction of State or local law enforcement), section 1512 (relating to tampering with a witness, victim, or an informant), section 1513 (relating to retaliating against a witness, victim, or an informant), section 1951 (relating to interference with commerce, robbery, or extortion), section 1952 (relating to racketeering), . . .
Keep in mind, even courts and judges are not immune from accountability. An Illinois court was declared a RICO enterprise (Operation Greylord).
18 USC § 876
Use of US Mail to extort money or other valuable item, or to threaten property, reputation or a person is a criminal act.
There may, also, be laws in your state. My state has the Profiteering Act.
There is more that could be added, and we are only getting your side. As such and for all we know, his threats may have been reaction to being treated poorly even after going an extra mile helping solve a problem someone [unknowingly] made. It may be you owe him a thanks, or even a thanks and an apology. Or not.