Short version is: Your Tutor is right, but his method is wrong.
So, you are trying to find the direction of the current, and you already have the direction of the magnetic and the force. Note that it is induced current, so you could use Fleming's right hand rule. That means F(the force) is to the left and B the, magnetic field (the x) is through the page(inwards). Using the right hand rule this means that the current is downwards, so take it as down E to A, meaning its clockwise.
Now when your tutor is . talking about the battery, that requires the left hand rule. So in this your trying to confirm F, which you know is left. your B(Magnetic field) is down. Making your current up from B to D.
However your tutors method isn't a great method to use. Left hand rule is usually meant to determine the direction of the force produced by magnetic field and electric current. You're trying to find the induced current, hence its more appropriate to use right hand rule, which is typically use for generators.
I hope you find this useful