No suspicion of heresy attached to it until 1710, when Hallett's son Joseph III became an assistant tutor, and brought in discussion of William Whiston's views.
Rumours spread as to the freedom of christological opinion permitted in the academy, until in September 1718 the Exeter assembly (a mixed body of Presbyterian and Congregationalist ministers) called for a declaration of belief in the Holy Trinity to be made by all its members.
In November the 13 trustees who held the property of the Exeter meeting-houses applied to their ministers for further assurances of orthodoxy, and failed to obtain them.
This body in May proposed that all its members should subscribe Thomas Bradbury's "gallery declaration" (see Salter's Hall controversy); at this point 56 did so, while 19 refused and seceded.
On 6 May a paper was drawn up, apparently by Hallett, whose signature stood first, in which the charges of Arianism and of baptising in the name of the Father only are disclaimed.