This answer is based on my experience with English probate records. While the probate process in the British colonies differed from that of the colonial power, the process was no doubt modelled on its British counterpart.
In England, it was customary for the testator to mention all his children in his will such that it was clear that none had been forgotten. In this way, the bequest was simply an acknowledgement. This was, theoretically, done so that a "forgotten" child did not have legal recourse to claim his share of the estate. It was thus not uncommon for a testator to leave one shilling, or another nominal sum, to certain children. This did not imply that he necessarily had a disagreement or lack of affection for those children, or intended to disinherit them. On the contrary, they had likely been provided for at marriage or when they came of age, had already inherited from grandparents, or had already had sufficient wealth or income.
I see no reason to conclude that the one dollar legacy implied they were minors. In fact, I might view it as evidence that they were adults. Minors would commonly be left more substantial legacies in the trust of another person. In the absence of making other provisions for their upbringing, I would say that it is unlikely they were minors.
The phrase "to be paid on their demand" also does not imply they were minors either. It was probably included to direct the executors that the legacy need not be paid unless those sons request it. This is consistent with my suggestion that these sons already had sufficient wealth (whether or not that was provided by their father) that they would likely not pursue or require payment of their $1 legacy.
In summary – no, do not conclude these children were minors.