A simple answer would be: in an 1C, biblical world context, the whole "house" would (if wealthy, which was not a very large % of the population) contain others beside the nuclear family, to include slaves and the like. It makes sense from a covenant-theology standpoint to recognize that many members under the head of a house would accept the direction and the beliefs of the head.
It should go without saying that refusal to believe or to be associated with the family's new religion--for example, in contrast to the joyful acceptance we find generally in the Philippian jailer's situation and in Cornelius'--should not see a coerced baptism. The idea of coerced circumcision in the case of Judaism is just as innately offensive, and must have been unheard of.
There's another observation to be made from the above inquiry, and that has to do with one of the presumptions embedded therein. "If we open up the ordinance [baptism] to non-believers within the household..." prejudices the case against the paedobaptist and in favor of the credobaptist. In fact, the typical paedobaptist doesn't consent to the idea that baptism belongs to unbelievers, any more than the typical credobaptist thinks it does. Both credobaptists and paedobaptists end up baptizing people who prove unbelievers. Reserving baptism to professors alone does not accomplish a purer assembly.
The issue is: when is the appropriate timing for which individuals to be baptized, based on what we think the Bible teaches? As has often been pointed out, the same allegations about the impropriety of paedobaptism may be lodged against paedo-circumcision on the same basis. Credobaptists have contended against the paedobaptists that circumcision and baptism are not analogous, that they do not have essentially the same meaning or function; but classic covenant theology will not budge on the contrary affirmation. Circumcision was a spiritual (not secular) sign for a spiritual (not secular) people, pointing to the reality of the covenant of grace prior to the arrival of Christ.
Both signs (baptism and circumcision) belong to faith, and not to any other; and therefore the timing of the sign's application may be determined by personal faith-profession in one instance, or (in the case of one who ought to be spoken for) on another person's behalf by the believer who presents his household for baptism along with himself. The faith of a parent is first put in the place of the minor, an element of which faith is trust in this promise of God: "I will be God to you, and to your children." It is a blessing and a great responsibility of every covenant child to make good use of the advantage of providential positioning, leading to his own profession of the faith in which he was raised.
I realize you may not agree with those statements, but my goal is less persuasion as to aid in understanding why a Presbyterian believes and acts as he does. So far as we believe it, OT circumcision was rightly possessed only by OT saints after Abraham's day, marking those truly who were of the faith of Abraham. Unbelievers of the OT age no more possessed right to circumcision than do unbelievers of the NT age possess right to baptism. And yet, children and other household members of the visible church (an institution for believers) of the OT were ordained to receive the external sign of membership along with their professing head. The concept was then what it is now: that signs applied externally should finally be in conformity with internal faith associated with the sign. Absent faith, the sign is ultimately a sign for condemnation as the promise of the sign is spurned rather than embraced.
So, to bring all of this back specifically to baptism, this rite is not by the Presbyterian being "opened to non-believers." It isn't for a rebellious child who frankly repudiates his parent's newfound faith, and will not accept being presented for baptism by them. It isn't for a theoretical modern-day servant, as it wasn't for an ancient slave lacking all intention of accepting the new faith of his master. Nor is it for liars or the deluded. It is for a helpless infant, a submissive child, or another radical subordinate or ward of a modern believer, who by this sign publicly acknowledges that all he is and possesses belongs to his faithful Savior. A new, adult believer takes baptism in connection to his faith, as it points to Christ; and the same believer claims baptism for his whole house that he intends to teach the fear and admonition of the Lord.
There is an expectation of teaching in connection with the gospel, and its reception and embrace. Should evidence of faith cease or never be seen, discipline blocks access to the Table of the Lord. We don't baptize people who refuse, implicitly or explicitly, to be Christ's disciples. It has never been otherwise with the church, either before Christ's coming recorded in the NT Gospels or in the present age. But (we say Scripture teaches) some are acknowledged as disciples outwardly before they ever had the freedom or potentially the inclination to refuse the identification. It's a pattern we Presbyterians see established for the church prior to the NC inauguration, and not changed upon the fullness come to be in the NC.