Illusory creature isn't a Minion and doesn't provide much information about attacking. It seems likely that it would take MAP, but doesn't specify so I'm not sure; it's additionally unclear if it shares MAP with the spellcaster.
The Multiple Attack Penalty is something that typically only applies to the individual creature making the attack, and is impacted by every check with the attack trait. Since illusory creatures can make Strikes, they would suffer the MAP as any other creature.
The more attacks you make beyond your first in a single turn, the less accurate you become, represented by the multiple attack penalty. The second time you use an attack action during your turn, you take a –5 penalty to your attack roll. The third time you attack, and on any subsequent attacks, you take a –10 penalty to your attack roll. Every check that has the attack trait counts toward your multiple attack penalty, including Strikes, spell attack rolls, certain skill actions like Shove, and many others.
There is one oddity under Mounted Combat where different creatures would share a MAP, though it would likely be difficult to ride an illusion.
You and your mount fight as a unit. Consequently, you share a multiple attack penalty. For example, if you Strike and then Command an Animal to have your mount Strike, your mount’s attack takes a –5 multiple attack penalty.