“Are you not well, sir?,” Jasperino says as soon as he hears that Alsemero is unwilling to depart for Malta. Jasperino knows something is obscuring Alsemero’s judgment. Alsemero responds a bit sarcastically saying, “Yes, Jasperino, unless there be some hidden malady within me that I understand not.” They have a very “brotherly” relationship despite Jasperino being a friend of Alsemero who is a nobleman. They are close enough for Jasperino to recognize that Alsemero is acting a bit strange.
We hear this all the time in the present. When someone is “love sick” and they are mixing logic and emotions which is obscuring perception. When you desire something so much you’ll neglect other sensible thoughts and actions to obtain it. This is usually the wrong way to go.
“The seamen call. Shall we board your trunks?,” says a servant. “No, not today,” responds Alsemero. Jasperino reminds him that it is the astrologically crucial day to leave and they should leave for a safe journey to Malta. Alsemero, against better judgment, refuses again.
When Beatrice-Joanna enters Alsemero greets and kisses her. Jasperino has a short aside to the audience in which he basically says “I knew it!” and “this cannot be good!” Jasperino’s entire point at the start of the play is that Alsemero’s new interest in Beatrice-Joanna is against better judgment and that it could have been avoided. Since Alsemero does not listen to his friend he has already foreshadowed his demise. All of which could have been avoided if he wasn’t so love sick and just boarded the ship.
Strictly speaking, I think Jasperino is primarily Alsemero’s servant, but he’s a servant who knows his master very well and might just as well be his friend, although in a subordinate relationship. He’s as alert to Alsemero’s needs as is De Flores to Beatrice’s. Had Jasperino not reported immediately to Alsemero when he hears Beatrice and De Flores talking, how much would Alsemero have figured out on his own?