There are a variety of outsourcing models in common use.
The supplier is based in the same region/country/timezone as the client. Example a UK client dealing with a UK supplier.
The majority of the supplier team is based offshore but a small number of supplier staff are located in the client region, possibly the same office for ease of communication and access. Example a UK client with a few UK based supplier staff and the main team based in India.
The supplier team is based in a near geographic region to the client, so time zone differences are small and travel times small. Example a UK client dealing with a European supplier.
The supplier is in a different timezone a significant distance from the client. benefits are often cost and team availability. Example a UK client dealing with an Indian supplier.