Take the bandaid off all together and do not apply antibacterial ointment unless you have an active infection. Both of these things can actually give 'germs' the environment they need to live and thrive. Bandaids keep the area 'wetter' than usual and the ointment just adds to that. Clean it twice a day with plain alcohol to keep it from being 'wet'. If you must put something over it to protect it, please just use a small amount of plain gauze and tie it on. Do not use tape or a bandaid to keep the gauze on the finger. You want to let it dry out, not keep it wet. Keeping it wet is a sure-fire way of working yourself into a full-blown bacterial infection as bacteria just love a moist environment.

The nail tech could have extended the nail plate with product, then applied a tip and then applied the product over the entire extension. That is, unless the injury was bloody or very 'wet'.