Wheelers are touching down mainwheels only in a level attitude, you then hold the tail up until you run out of forward stick. Wheelers are particularly useful in gusty conditions and many tailwheel pilots prefer them for crosswinds as it keeps the rudder in the slipstream until the tail finally drops at a
very low speed. IMHO anyone converting to tailwheel should at least learn this technique even if you choose not to use it (I will not sign a tailwheel endorsement off without it).
n.b. Touch and goes will normally be acceptable for TO & Ldgs - or had they specified that tis was not OK?