Problem with my teleporting of players?

The problem with your teleporting is that when you do it, players the variable doesn't update, so when a player joins, it still says that there is only 1 player. What you need to do is replace all the players with game:GetService("Players"):GetPlayers()

#Final Product

local serverStorage = game:GetService("ServerStorage")

local maps = serverStorage:WaitForChild("Maps"):GetChildren()
local statusText = serverStorage:WaitForChild("statusText")

while wait(1) do
    for intermissionTime = 10, 1, -1 do
        statusText.Value = intermissionTime .. " until a new round starts!"
        wait(1)
    end

    statusText.Value = "Choosing a map..."
    wait(3)

    repeat
        chosenMap = maps[math.random(1, #maps)]
    until chosenMap.Name ~= oldMap

    statusText.Value = "The chosen map is " .. chosenMap.Name .. " by " .. chosenMap.Creator.Value .. "!"

    local chosen = chosenMap:Clone()
    chosen.Parent = workspace
    wait(3)

    for waitTime = 5, 1, -1 do
        statusText.Value = "Teleporting players in... " .. waitTime
        wait(1)
    end

    for i, v in pairs(game:GetService("Players"):GetPlayers()) do
        local spawns = chosen:FindFirstChild("Spawns"):GetChildren()
        v.won.Value = false
        v.Character.Humanoid.WalkSpeed = 0
        v.Character:MoveTo(spawns[i].Position)
    end

    wait(3)
    statusText.Value = "All players have 60 seconds to finish. Go!"

    for i, v in pairs(players) do
        v.Character.Humanoid.WalkSpeed = 16
    end

    roundTime = 60
    dead = 0
    roundtimeReached = false
    playerhasWon = false
    allplayersDead = false

    while wait(1) and roundTime > 0 do
        for i, v in pairs(players) do
            if v.Character.Humanoid.Health == 0 then
                dead = dead + 1
                if dead >= #players then
                    allplayersDead = true
                elseif v.won.Value then
                    playerhasWon = true
                elseif roundTime > 0 then
                    roundtimeReached = false
                end
            end
        end
        statusText.Value = "You have " .. roundTime .. " seconds left!"
        roundTime = roundTime - 1
    end

    oldMap = chosenMap.Name
    chosenMap:Destroy()

    if playerhasWon then
        wait(3)
        statusText.Value = "A player has won!"
        for i, v in pairs(game:GetService("Players"):GetPlayers()) do
            if v.won.Value then
                v.leaderstats.Points.Value = v.leaderstats.Points.Value + 10
            end
        end
    elseif allplayersDead then
        wait(3)
        statusText.Value = "Everyone has died..."
    elseif roundtimeReached then
        wait(3)
        statusText.Value = "The round time is up!"
    end
end

Hope it helps!