Is there a way to fix the problem of the script subtracting 1 when the IntValue hits to 0?

Un-necessary to have a repeat within a while loop. You can simply edit your while loop by replacing the true with the conditional...

local Inter = Instance.new("IntValue") -- Creates the Value
Inter.Parent = game.Workspace
Inter.Name = ("Intermission")
Inter.Value = 10

while Inter.Value > 0 do
    wait(1)
    Inter.Value = Inter.Value - 1
end

@Uroxus's answer is the correct way to do it.

Below works but isn't correct.

local Inter = Instance.new("NumberValue") -- Creates the Value
Inter.Parent = game.Workspace
Inter.Name = ("Intermission")
Inter.Value = 10

repeat
    if Inter.Value ~= 0 then
        wait(1)
        Inter.Value = Inter.Value -1
    end
until Inter.Value == 0

A repeat loop checks its condition last, meaning it will always run the code inside at least once. I'm not sure what you're trying to do, but this would fix that problem:

local Inter = Instance.new("IntValue") -- Creates the Value
Inter.Parent = game.Workspace
Inter.Name = ("Intermission")
Inter.Value = 10

while true do
    while Inter.Value ~= 0 do
        wait(1)
        Inter.Value = Inter.Value -1
    end
    wait()
end

However this is bad code. Instead a simple for loop would do:

local Inter = Instance.new("IntValue") -- Creates the Value
Inter.Parent = game.Workspace
Inter.Name = ("Intermission")
Inter.Value = 10

for i = Inter.Value, 0, -1 do
    wait(1)
    Inter.Value = i
end

If this isn't what you wanted please explain in greater detail what you want the code to do.

local Inter = Instance.new("IntValue") -- Creates the Value

Inter.Parent = game.Workspace

Inter.Name = ("Intermission")

Inter.Value = 10

    repeat
        wait(1)
        Inter.Value = Inter.Value -1
    until Inter.Value == 0

Its an infinite loop. The while true do part kept repeating the repeat wait(1) until part.