Answer:
The colonists considered themselves British subjects, becuase many of the colonists are either from Britain, or were of British settler descent.
Step-by-step explanation:
The ideal of "America" was yet to be concieved, as America was only recognized by France in 1778, with the majority recognizing in the 1780s, spanning from 1782 - 1783, ending with Great Britain recognizing the US with the Treaty of Paris. Until then, they were still regarded as break-away British subjects.
All countries before they are officially a country go through this process, with nations recognizing the legal government, and meeting the definition of a country. Until the US is completely under it's own governmental jurisidiction without British control, they are only considered break-away.
This is why, having a self-sustaining government + economy, and the recognition of other countries (especially global powers) are essential in creating a self-sufficient country.