So what is the meaning of the Irish phrase Tis Herself? 

The Irish term "Tis Herself" is an affectionate expression in both the Irish and Scottish language, denoting a woman of importance, usually the lady of the house. It is suggestive of someone announcing the appearance of royalty. 'Tis herself is usually meant in jest, for a female who thinks she is more important than she really is. Like a real Irish Queen or Irish Princess.  Someone who deserves to wear an Irish tiara. It's sort of a joke. But as we all know every lady of the house is really the Queen of the home.

Why do the Irish say himself?

In Scottish and Irish English, “himself”—and “herself”—are used to refer to someone of importance, like the lord of the castle or the master of the house.

What does tis himself mean?

The phrase "himself" might be reserved for more than one male individual in the same family at the same time. Tis himself is an affectionate expression that is used in colloquial Irish to refer to the head of the household.