Possibles:
if the ground below where you've replanted the azaleas is packed hard a few inches under the fluffy top soil then your watering could be forming a swamp. Azaleas like to have a moist soil but start to rot in heavily wet soil. Take out the azaleas, break up the hard pan and replant on a slight cone of soil so water drains away gently.

If the area is in full sun during the day - or gets windy - install some temporary shelter using burlap or old sheets. If you damp the cloth it will keep the air around the plants cooler and moist and stop them losing water faster than they can get it through their shortened roots. It can take several years before the azaleas will be firm in the ground again, so care will be needed over that time to not dig deeply around them.

If the parts that are wilting are new shoots that haven't hardened off then you could trim them back to the older wood. You will probably lose the next season's flowers - but that's happening already if the shoots wilt and don't recover.

One thing that may help ongoing recovery is to ensure there is no grass growing under the azaleas. Instead, cover the ground up to 3" deep with a mix of ancient steer manure and weathered bark chips. Keep it about two inches back from the trunks of the plants so no fungus can start.

If these are evergreen azaleas, after a while they form their own mulch as leaves and flowers die/drop on the ground, but fresh mulch with a little nouishment is usually welcome and helps produce more flowers.

Another thing to consider is that perhaps these azaleas were replanted in their new location too deeply. Azaleas/rhododendrons are very shallow rooted and dislike deep planting. Rapid wilting is often a signal that this has occurred.

A place out of full sun (light shade) is best for them so if the move was from filtered light to full, that may be part of the trouble. BTW, you could water a lot daily and they'd be quite happy - azaleas need and want lots of water.