Each unit of a player has “vision” property that defines which tiles are observed by the unit. Tile on a map is considered visible by a unit if distance to a tile is less than “vision” property of the unit. Let's consider tile coordinates as (Trow, Tcolumn) and unit located at (Urow, Ucolumn).
Tile is visible if and only if (Trow - Urow)2 + (Tcolumn - Ucolumn)2 ≤ Vision2
All tiles visible by a unit form visibility area of the unit (kind of a pixelated circle). Combined visibility areas of all units form visibility area of the player. Server's responsibility is to send up to date information for all tiles in player's visibility area. It includes tile types and units located on those tiles.
Tiles which were visible before at least once, but no longer visible at the current moment define so called “fog of war” area of the player. Client knows type of the tile from the last time it was part of visibility area, but no longer receives any updates from the server. If tile type is changed (which is never happening in Season 0) or new object appears on a tile, player won't get any updates.
Fog of war may be used by a client to construct paths for units, because type of tiles in fog of war is known and is not changing in Season 0. However, certain tiles in fog of war may be occupied by other units and in the future type of tile may change, so it is always responsibility of the client to verify that path is valid as unit moves and recalculate it if needed.
Zombie unit located on a map. Tiles in visibility area are lighter and tiles in fog of war are darker in color. Black tiles have never been discovered yet and they may be of any kind, server does not share any data on them.