question about being banned

i was recently banned from a server by admin all i did was teleport nothing crazy but still cheating i can understand. my question is if admin banned me for teleporting could he show battleeye at sometime for global ban or is it just from that server?

also if i use a hack then disable it does it show up on the log more? or once i enable a hack should i just leave it on?

If the server has battleye on then you will probably receive a global ban, or maybe it was just an admin ban and you got lucky.