The problem is that you haven't given any reason to see OIKOS as anything other than the definition given. Here it is, with a small section from it

OIKOS Formula

"The phrase 'he and his (whole) house' denotes the complete family; normally husband, wife and children. In no single case is the term 'house' restricted to the adult members of the house, though on the other hand children alone may be mentioned when the whole house is meant. Whilst slaves are very often not reckoned as part of the 'house,' the inclusion of the children is taken for granted. Indeed, the Old Testament repeatedly lays special emphasis on the very smallest being reckoned in. Since the primitive Church takes the phrase over as a firmly established biblical expression, the statement 'it includes small children as well as others' applies to its employment in the New Testament as well" (Jeremias, p. 24).
(emphasis mine)

Act 16:30 And brought them out, and said, Sirs, what must I do to be saved?
Act 16:31 And they said, Believe on the Lord Jesus Christ, and thou shalt be saved, and thy house.
Act 16:32 And they spake unto him the word of the Lord, and to all that were in his house.
Act 16:33 And he took them the same hour of the night, and washed their stripes; and was baptized, he and all his, straightway.
Act 16:34 And when he had brought them into his house, he set meat before them, and rejoiced, believing in God with all his house.

The passage does not give ages, and your example has only adults. Although I am not a language expert, I am unsure that believed must apply to everybody.

God bless,