WT says:
*** w96 10/15 p. 21 Father and Elder—Fulfilling Both Roles ***
“Having Believing Children”
5 When instructing Titus to appoint overseers in the Cretan congregations, Paul stipulated: “If there is any man free from accusation, a husband of one wife, having believing children that were not under a charge of debauchery nor unruly. For an overseer must be free from accusation as God’s steward.” Just what is meant by the requirement “having believing children”?—Titus 1:6, 7.
6 The term “believing children” refers to youngsters who have already dedicated their lives to Jehovah and have been baptized or to young ones who are progressing toward dedication and baptism. The members of a congregation expect elders’ children to be generally well-behaved and obedient. It should be apparent that an elder is doing all that he can to build up faith in his children. King Solomon wrote: “Train up a boy according to the way for him; even when he grows old he will not turn aside from it.” (Proverbs 22:6) But what if a youth who has received such training refuses to serve Jehovah or even commits a gross wrong?
7 It is evident that the above-quoted proverb is not stating a hard-and-fast rule. It does not annul the principle of free will. (Deuteronomy 30:15, 16, 19) When a son or a daughter reaches the age of responsibility, he or she must make a personal decision with regard to dedication and baptism. If an elder has clearly given needed spiritual help, guidance, and discipline, yet the youth does not choose to serve Jehovah, the father is not automatically disqualified from serving as an overseer. On the other hand, if an elder has several minor children living at home who, one after the other, become spiritually sick and get into trouble, he might no longer be considered to be “a man presiding over his own household in a fine manner.” (1 Timothy 3:4) The point is, it should be manifest that an overseer is doing his best to have ‘believing children that are not under a charge of debauchery nor unruly.’
Although the wording and interpretation could be vague, the usual black-and-white interpretation I've encountered is that if his kids aren't dunked by 16, questions are raised. (Actually, that was the case with me.) The wording that kids can choose for themselves when they're of age, involves the kids that are already grown when the parents learn "the truth". The WT words it like the elder may have a dfd child at home and he still may serve, but I've never seen it happen. I'd love to hear some stories of how that's happened and been justified somehow. There are plenty of strange cases in Watchtowerland.