Ujiri is not rushing ANYTHING - nor should he.
He's not going to do his work with any urgency or panic because that's not how good decisions are made (see Brian Colangelo). No, i expect him to sit on his hands for a while and just watch and get a really good understanding of exactly what this team needs and what the best moves are. If he doesn't have a coach lined up and ready to take the job (which i suspect he doesn't) there's no point to firing Casey yet.
Best thing i can suggest is to not get caught up in success this season.