No. It is perfectly normal that the CIA would be tailing Oswald and even be in direct contact trying to turn him into a double agent.
Oswald was an agent recruited and maintained by James Jesus Angleton, the CIA’s Chief of Counterintelligence.
The CIA taught Oswald Russian and then sent him into Russia (along with several other Americans btw) as a spy.
The notion that Oswald was a Communist was the cover story.
I don’t think the Russians bought it—kinda surprising any Americans were fooled either.
One amusing “clue” was that after Oswald was arrested in Dallas he asked for an attorney named Abt.
(Background: Oswald had tried to get his “Fair Play for Cuba” operation approved by the HQ of the Communist Party USA. They laughed at him—Oswald was an obvious agent provocateur.)
Nobody had ever heard of that attorney.
Abt was the in-house attorney for the Communist Party of the USA at the time—and of course would want nothing to do with Oswald.
It was Oswald trying to assure the CIA that he was still on the undercover “team”.
Oswald was not certain he had been set up and betrayed until Ruby’s bullet was heading straight at him.
If you want to read about Oswald from someone who actually knew him well (his mistress) this is the book to read:
https://www.amazon.com/Me-Lee-Came-Harvey-Oswald/dp/1936296373