The cartel has orders to bring Nacho in alive for information on who he works for. If he is killed by someone else it may look suspicious, Nacho being silenced while Gus is the prime suspect for the attack on Lalo doesn't look good for Gus. However, if Nacho is killed during a shootout with the cartel, the cartel leaders will likely come to the conclusion that their men were too aggressive and made a mistake by accidentally killing Nacho. This way it doesn't look like Nacho was silenced by anyone.
There was a guy hired to watch Nacho and kill him whenever the cartel showed up to make this happen. Nacho spots him and ruins Gus' plan. Notice how the guy watching him gets a call right after Nacho tells Tyrus he's leaving. Calling Tyrus was Nacho's test, so he can find out whether the guy watching him works for Gus and has been hired to kill Nacho, but only after the cartel arrive.
Nacho keeps trying to call Mike because he trusts Mike, not Gus. He knows Mike wouldn't approve of killing him, but that Gus wouldn't hesitate to do so. Mike wouldn't answer Nacho's call because he was told not to interfere with Gus' plan.