This is a very individual question and depends very much on the character of the animal in question. Some Chihuahuas get along with little velvet paws right away, others want to chase cats, play with them, simply accept them or, under certain circumstances, ignore them and ignore the cat.
It also depends on whether the Chihuahua has already met cats from the breeder. If so, he’ll probably see them as something “normal” and remain cool with them. Provided his experiences with house tigers were positive. So socialization plays a big part in whether or not the Chihuahua gets along with cats in the end.
The same applies, of course, to the house tiger. Is the cat dog experienced? Is she generally easygoing or hostile?
Please note that an adult cat can be quite dangerous to a Chihuahua or Chihuahua puppy. The reverse is also true.