Cessna 208 Caravan Amphibian instructor reported a gear up landing during landing phase.

Narrative

During a training event of a new hire; a mistake in the landing gear checks plus the failure of the landing gear position aural alarm resulted in a RWY landing with the gear up.A new hire (land 208) captain under training had just finished his training prior his check-ride; when the regular land version 208 we were using for training experienced a grounding technical problem.Company decision was made to perform a training familiarization flight on the amphibian version (one plane was available) to allow the new hire to perform his check-ride with that version in order not to delay his subsequent line introduction training at his home base.A familiarization flight was scheduled (and performed) with the intent of allowing the trainee to become familiar with the different trim forces; heavier inertia; different cockpit height and the addition of the landing gear system.During the second pattern; the trainee failed to lower the gear when discussed and prompted; but a combination of turbulences and strong wind causing drifting; forced me to intervene in the controls and diverted my attention from the landing gear task. On base to final I performed the landing gear checks loudly and by touching the handle and verifying the lights (the mirrors checks are difficult in the right seat because of the radome obscuring the sight of the mirror); but probably because of a combination of the sun blinding me (we turned directly into the sun) and confirmation bias (I had performed approximately 50 landings with the gear confirmed down in the previous 3 days of training) I failed to notice the gear incorrectly positioned. Despite having flown a standard pattern with the appropriate speeds and profile; the aural gear warning failed to operate. My confirmation bias was so strong that after we landed; I failed to recognize what have happened and I thought the trainee had the brakes locked during the touch-down therefore the right and left tires had failed during the roll. That was I told the TWR.