It's very unlikely that a new guitar from a decent manufacturer like Ibanez is going to have a faulty tuner. For it to have several is just about impossible.
Without actually seeing the guitar it's impossible to be sure but, from what you say, the most likely cause is that the strings aren't attached properly at the tuners and they are slipping - when you turn the tuner the pitch goes up, the tension increases and the string slips back down in pitch again.
Again though, this seems unlikely with a new guitar unless someone replaced or interfered with the strings.
Whatever you do, don't try changing or re-attaching the strings unless you're sure that's the problem and you know what you're doing. If in doubt, seek help from another player.
Added, my answer assumes that the pitch of the note really is going up and then dropping again - you don't need a tuner to tell you this, you'll hear it. I thought about the strings sticking in the nut slots but that wouldn't cause the pitch to go up and then drop again. Also, it's usually the wound strings that stick, not the plain ones.
It would be GREAT when you get it sorted if you updated your question or posted a comment to tell us what the problem really was.