Why can I still use "commands" when i'm not in the admins table?

The reason is because you never actually checked if they are in the admin array.

All you did was:

for i,v in pairs(admins) do
plr.Chatted:connect(function(msg)
--blah
end)
end

In for i,v in pairs(admins) do you are merely only iterating through the table, but not even giving the script anything to do for each item in the table.

That's like saying in real life:

For everyone here.

Alright. Great. You've told us that the subject is 'Everyone' but you haven't told us what to do with the subject.

If you are making this an admin system, then you can change your code to the following:

admins = {"d"}

function findPlayer(name)
    for _, player in ipairs(game.Players:GetPlayers()) do
        if player.Name:lower() == name:lower() then
            return player
        end
    end
end

function isAdmin(plr)
for _,v in pairs(admins) do
if v:lower() == plr.Name:lower() then
return true
end
end
return false
end

game.Players.PlayerAdded:connect(function(plr)
   if isAdmin(plr) then
        plr.Chatted:connect(function(msg)
          if msg:sub(1,5) == ";kill" then
             victim = findPlayer(msg:sub(7))
             if victim and victim.Character then
                victim.Character:BreakJoints()
            end
          end
      end)
   end
end)