In real life, it is well-known that Hervé Villechaize left the show (https://www.tvguide.com/news/question-did-tattoo-65287/) due to a salary dispute, but did they ever explain within the show why the character left?

No explanation was given, according to TV Tropes (https://tvtropes.org/pmwiki/pmwiki.php/Series/FantasyIsland):
What Happened to the Mouse?


During the Tattoo/Julie year we see Julie see the plane and run off to greet it. While some of the episodes with Tattoo give a short mention that Julie is busy with another fantasy, others show her leave to greet the plane, then disappear completely from that episode without explanation.
We never find out why Julie and Tattoo leave before the Lawrence episodes.


Was the audience back then, basically left to assume that Tattoo had either passed away or moved on to more lucrative positions?

I don't think it was explained. When you openly quarrel with producers and "hit" on every female guest during the taping of FI, then your character might just disappear.

I remember that the tabloids loved Herve because he was embroiled in some sort of dilemma every month.

Actor Wendy Schaal said that Hervé Villechaize wasn't pleased when she joined the cast of Fantasy Island (https://www.metv.com/stories/actor-wendy-schaal-said-that-herv-villechaize-wasnt-pleased-when-she-joined-the-cast-of-fantasy-island)

"I don’t think he disliked me as a person, but I think he felt my presence (on the show) was unfair to him."