While the US market is large, the rest of the world is also impacted by medical device recalls and drug recalls. Whether it is a US supplier selling in Europe, or an Israeli pharmaceutical company supplying Japan, the time of action of medical device recalls and drug recalls are similar in rule.
Most every nation (or groups of nations) has their own specific medical device or pharmaceutical regulations, with appropriate governmental bodies to control those markets. These bodies have jurisdiction over domestic manufactures in addition as import/export activities by manufacturers or distributors.
Canada has a ministry known as Health Canada. Korea has the Korean FDA (KFDA). Ireland has the Irish Medicines Board. Each of these nations have their own requirements, which creates a burden for manufacturers trying to send product to those markets. In some situations, nations will accept the US FDA as a recognized authority, essentially agreeing that if it a product is safe in the US then it is safe for them. However, this is not the case in most places.
In the European Union (EU), there is a central law called the Medical Device Directive honored by all member states. Each nation has their own equivalent to the FDA (in Germany, for example, it is called BfArM, or Bundesinstitut fur Arzneimittel und Medizinprodukte), and those bodies control products being used in their areas. If negative events or a product ingemination occurs within Germany, BfArM will collect that information and deal with the manufacturer. All of these bodies proportion information, so a ingemination in Germany could cause inquires from the French version of the FDA, and frequently manufacturers proactively inform all EU member states of a medical device ingemination or drug ingemination, already if the recalled product was not present in a particular EU nation.
So a US based manufacturer answers to the FDA, in addition as each definite regulatory body in any nation where their product is sold. In fact, in a case where a product is made in the US, and only sold outside the US, the FDA will nevertheless be notified of any ingemination action and they will track that information just as if the ingemination was a domestic issue.
Medical device litigation or drug litigation in those nations will, of course, conform to local laws, and manufacturers are bound to the laws and customs of those markets. Simply being physically outside of the borders of a country does not relieve one of responsibility to conform to legal requirements.