Are the tenses correct in this text?
The tenses are perfect but there are other issues. You don’t refer to cats as boy and girl. Usually you would say male and female. A cat doesn’t “always” catch mice. Also you should say “the other” not “another”. And you sleep by a window.
I have two cats. One of them, a female, regularly catches mice. The other, a male, has never caught a mouse. He’s very lazy and often sleeps by the window.
I have two cats. The female catches mice. The male, never. He’s lazy and seems to do nothing but sleep by the window. (Spoken)
If you want to use “always”, you would typically say “The female is always catching mice”