Γεια σου Ιάκοβε
You are correct, a male person will say (for himself) “είμαι κουρασμένος”, while when refering to another female, he will say “είναι κουρασμένη”.
Είμαι means I am.
Είναι means he/she/it is.
For a male person who is tired we say κουρασμένος.
For a female person who is tired we say κουρασμένη.
The word changes depending on the gender of the person who is tired.
It is irrelevant who says it. It could be be a male, a female, a text writen in stone or a computer with artificial inteligence. It does not matter.