James Haeck on D&D Writing | Dungeons & Dragons
Above is the podcast that discusses this.
To paraphrase:
Being invisible does not make others unaware of you and your position. You only become hidden if you take the Hide action (i.e. make a Stealth check, which you can always do if you are invisible) and you beat the Passive Perception of your target.
At the DMs discretion, some circumstances might make possible for an invisible creature to need not a Stealth check to make himself both unseen
and unheard (the definition of hidden). Such circumstances may be a significant distraction and fair distance. In those cases, always at the DM approval, an invisible creature benefits from being hidden even without a Stealth check.
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A Monk attacking someone and then sprinting off in the same turn, is not such an outlier, and neither is an Imp turning invisible and flying off on its turn.
The round they do this, nearby creatures can fire a few shots at the sound of them moving away, or swing blindly in their general vicinity (attack at disadvantage). Nearby creatures dont know their location with sufficient precision to target them with most spells (barring AoE spells) or to make opportunity attacks agianst them, or to target them with many special abilities.
If on their next turn, they're 100' or so away and they want to be quiet and Hide, I'd let them roll with advantage to the check due to distance.