Ilbranteloth
Explorer
The ones who are in the middle of combat and can only do one thing at a time, so they just cast a spell and haven't had time to get around to hiding yet. They probably have future intent to hide, but they aren't actually trying to hide yet.
I'd be okay with a house rule that lets someone try to hide as soon as they went invisible, if the DM was insistent, but I would prefer to play in a world where escaping combat isn't that easy. The default rules basically make it impossible for a spellcaster to flee from the party, since they'd have to weather an entire round worth of attacks between going invisible and hiding, and that sounds great to me as a player.
There really isn't a need to make a Stealth check once they are invisible. They can simply move.
"When you attack a target that you can't see, you have disadvantage on the attack roll...If the target isn't in the location you targeted, you automatically miss."
Even if you hear them, people are quite poor at determining the location of somebody/something by sound alone. This is relatively easy to handle with a grid, since the DM will know which space the invisible creature is in, and can tell you if you hear them, the general direction, but then you've still got to select a specific square to attack.
In Theater-of-the-Mind it's a bit more difficult. In that case I use the attacker's passive Wisdom (Perception) against the invisible creature's passive Dexterity (Stealth) with whatever modifiers are appropriate to determine whether they are targeting the correct location. The same approach can be used with a grid, in which the DM can tell you which square you think is the right one.
I would apply disadvantage to the Wisdom (Perception) check, but you could just as easily grant advantage to the Dexterity (Stealth) score with similar results.