Oswald was known to have numerous contacts with the Russians and he lived there for 4 years.

And he was on the CIA and FBI radar because of that, he would be a terrible agent because of that. Keep in mind the Soviet didn't trust him when he tried to defect, they flat out rejected him at first. When Oswald tried to defect, he offered up information on the radar the US Marines were using at the time, the kind he was trained on. Keep in mind the US Marine Corps gets left overs from the other Branches so the radar he was trained on was already outdated and in the process of being phased out. So the reason for them to reject him, is because he might be a CIA spy. Eventually they did allow him to become a Soviet citizen, but they gave him really crappy living and working arrangements. Most likely because they didn't trust him. And Oswald hated it, he even wrote in his own diary how miserable he was. Oswald thought he would be rewarded for defecting and providing Intel on Marine Corps radar in Japan. But the Soviets didn't trust him and made sure he was just a common worker.

My guess is the reason he was reporting to the KGB in Mexico City was because he was trying to offer his services to the KGB, because he did try to Kill a US General before he made his trip south of the border. KGB most likely reject him(not surprisingly again). The US and the USSR had an understanding, that KGB, CIA, Military Officers and their families were off limits. But Oswald trying to kill General Edwin Walker, set a precedent that it's open season all of these once protected individuals.