I don't know what his innings limit is this season, but I expect we'll see him up sooner rather than later.
He went 123 innings last year, so I imagine they will bump him up to 140-160 this year and consider him ready for a full season workload if he pitches through September.
Looking at his game log, he's had 1 brilliant start this season, 5/28, followed by one of his 2 very good starts 6/4. both 7 inning starts, one with 2 hits, 1 walk, 6 Ks, 0 runs, the next other with 5 hits, 2 walks, 10 Ks, 1 run. Next best start would be 5/11, 5.2 IP, 4 hits, 1 BB, 1 HBP, 6 Ks, 2 runs (1 ER), or weird on on 4/30 (5.1 IP shutout, 0 hits, but 3 BB, an HBP, and 1 K) . The rest are 4-5 inning starts, not much to speak of. WHIP of 1.5 -2.0, just a K or fewer an inning, is not dominating. He's suppressing homers (3 in 57 IP), but gave up 2 in his second to last start on 6/10.
https://www.fangraphs.com/players/steven-cavalli/sa3014421/game-log?position=P&season=What you want to see before a call up is a string of games like 5/28 or 6/4. I want 6+ innings, >6 Ks, WHIP < or = 1, < or = 2 runs. I want 4 of those in no more than 5 starts. Then I'd start to think he has no more to learn at AAA. I want to see domination in AAA before I feed him up to MLB in a lost season.