The flight path didn't go over "The West". Turkey looks to be the only US allied country he flew over.

Expanded from an earlier answer of mine

There were concerns in both the Soviet satellite and manned space programs over whether or not the spacecraft would overshoot or undershoot its landing trajectory and end up in "foreign territory." The early unmanned systems had a device installed that would trigger a self-destruct mechanism if a g-sensor did not activate at a certain point in the reentry phase. The self-destruct was timed sixty hours after landing. This system was somewhat haphazard as it led to problems in the Vostok testing program. Malfunctions in Korabl-Sputnik 3's launch actually triggered this self-destruct system, killing the occupants of the spacecraft, the spacedogs Pchyolka and Mushka. The Soviets reported to the press that the spacecraft burned up because of incorrect altitude, but it was likely the self-destruct mechanism was to blame. The follow-up launch for Korabl-Sputnik 3 on 22 December 1960 had a similar problem when its third stage malfunctioned, triggering the emergency escape system. The capsule undershot the landing zone and ended up in a remote corner of Siberia. Fortunately for the spacedogs Kometa and Shutka, the failure of the third stage had burned through the wiring for the explosives and the dogs were recovered unharmed, albeit quite cold, after the 60 hour window.

The problems inherent with an automated self-destruct system, which the spacedogs found out to their detriment, made it quite problematic for manned spaceflight. A State Commission chaired by Central Committee member Konstantin Rudnev on 28 March 1961 discussed the possibility of Vostok 1 ending up in non-Soviet territory. With the sole exception of the KGB representative Peter Ivanovitch lvashutin, the Commission, including Korolev, decided against an emergency self-destruct device. The Commission's contingency plans did consider a landing in "foreign territory" and gave a nebulous set of instructions for the cosmonaut:

In the event of a forced landing in foreign territory or the rescue of the cosmonaut by a foreign ship. the cosmonaut has appropriate instructions. In addition to a ten day supply of food and water, the cosmonaut's cabin is outfitted with a portable emergency supply of food and water that will last for 3 days, and also means of radio-communications and the "Peleng" transmitter whose signals can be used to determine the landing site of the cosmonaut. The satellite ship is not equipped with a system for emergency destruction of the descent apparatus.

By providing the cosmonaut with enough food and water to survive for an extended period of time, the Commission based its contingency strategy upon the survival of the cosmonaut. In contrast to the secrecy surrounding prior space launches, the Soviet news agency TASS would publish a report of Vostok's flight as soon as it reached orbit. This way if Vostok went off course, the Soviet press was primed to frame any Western interference or detention as a diplomatic incident and prevent the cosmonaut from being declared a spy.

As the above peregrinations show, spaceflight posed a number of thorny legal questions. The legal position of spaceflight and its associated emergencies is a very murky one for international law. The advent of manned spaceflight superseded a number of laws regarding the legality of overflight and the nature of sovereign territory. For example, the 1944 Chicago Convention helped establish the groundwork for International Civil Aviation Organization- ICAO which clarified a number of the basic rules for emergency landings and what constituted an infringement of national airspace. The ICAO established that the airspace above national boundaries is national territory, there can be no neutral crossing of this territory. Space vehicles sidestepped this legal precept. De Gaulle demonstrated this facet of outer space to Khrushchev when the latter went on a harangue about the Gary Powers U-2 incident at the Paris Peace summit. He told the Soviet premier "yesterday that satellite you launched just before you left Moscow to impress us overflew the sky of France eighteen times without my permission. How do I know that you did not have cameras aboard while taking pictures of my country?" upon which Khrushchev flubbed his answer. As laws regarding space have evolved, a general legal consensus has emerged that space is neutral territory, unlike that of the atmosphere.

This of course poses the question about what about emergency landings which the Commission for Vostok-1 was concerned about. As space vehicles transitioned between atmosphere and space, they occupied an indeterminate legal zone. The UN sought to clarify matters in the late 1960s with two international treaties that outline both the responsibilities of the state that launched vehicle and the wider international community as a whole. The 1967 Treaty on Principles Governing the Activities of States in the Exploration and Use of Outer Space, including the Moon and Other Celestial Bodies maintained the idea that astronauts and space exploration as a whole was a human endeavor that transcended national boundaries. Article 4 of the 1967 UN Resolution for Agreement on the Rescue of Astronauts, the Return of Astronauts and the Return of Objects Launched into Outer Space established that in case of emergency, all signatories of the resolution would:

If, owing to accident, distress, emergency or unintended landing, the personnel of a spacecraft land in territory under the jurisdiction of a Contracting Party or have been found on the high seas or in any other place not under the jurisdiction of any State, they shall be safely and promptly returned to representatives of the launching authority.

Responsibility for cleanup and damages incurred by a wayward launch or deorbit were placed at the feet of the launching power.

Of course, these UN resolutions are dependent upon self-enforcement and whether or not either superpower would have upheld them with regards to top-secret space equipment is venturing into what-if territory. However, it is likely that they would have obeyed the strictures of these late 1960s agreements as they fit within the established paradigms of international rescue pioneered by the ICAO.

Source

Siddiqi, Asif A. Challenge to Apollo The Soviet Union and the Space Race, 1945-1974. Washington, D.C.: National Aeronautics and Space Administration, NASA History Div., Office of Policy and Plans, 2000.