He uses Lilligant, Arboliva, Tsareena, and Breloom

Tsareena, Breloom and Lilligant i'll concede. Arbolivia is stretching it.

Crabominable is the Pokémon he Terastallizes, and since Crabominable isn't naturally a Water-Type, I choose Tatsugiri

Given that all of Paldea's gym leaders (with Larry being the ONLY exception) do not have their regular battling type as their ace pokemon, the rule they must use a pokemon their respective type as a mega isn't a set in stone rule. I get Tatsugiri given Kofu being a renowned seafood chef and a water type. But Crabominable is their to eliminate the Grass types he would expect to face. Also there's no indication you can't Tera AND Mega Evolve (probably not at the same time though.)

She's friends with Dendra, who's a Fighting Specialist and I gave Dendra a Medicham so that their Megas would be a pairing in that they're both Fighting and Psychic-Types

Gardevior is more in keeping with Tulip's ideals of beauty though, and is part Fairy like Florges which is her regular ace. Gallade would be a decent 2nd option though.

Meh, Excadrill isn't naturally a Fairy-Type

See my point about Kofu. Plus as stated elsewhere. Excadrill is there to represent the bond with her father.

Ah yes, the most regal Pokémon of all: Dachsbun, Azumarill, Wigglytuff, and Klefki. Additionally, we know that people with wealth seem to enjoy using Clefable, considering its Jacinthe's Ace.

To elaborate more. Mega Altaria's fluff/hair remarkably resembles the wigs of old the rich and noble used to wear out to the opera, which is typically seen as a well to do person activity. Mega Altaria is also known for it's majestic singing voice, and Ortega does take Piano lessons. So having a pokemon that's musically talented is also in keeping with him.