Your question seems to imply that the Regency membership was under the influence or control of Iturbide, but according to Bancroft, at this later time these seats were reorganized by the Congress, who were in ongoing conflict with Iturbide, essentially attempting to stack it against Iturbide. From Bancroft, History of Mexico 1804-1822, pg 769 (emphasis mine).
As for the congress its hostility toward him was now openly expressed.
By decree of the 11th of April the regency was reorganized the bishop
of Puebla Manuel de la Bárcena and Velazquez de Leon who were too
evidently subservient to Iturbide being removed from their positions
and their places supplied by the conde de Casa de Heras Soto, Doctor
Miguel Valentin and Nicolás Bravo in whom the congress placed the
utmost confidence. Yañez was retained in his seat for the reason of
Iturbide's known enmity to him.
Wikipedia has a paragraph concerning this conflict between Iturbide and the congress for a little more background to the situation:
In the meantime, the governing junta that Iturbide headed convened a
constituent congress to set up the new government. The new government
had indirect representation, based on the Cadiz model, but the Plan of
Iguala and the Treaty of Córdoba were clear that the order of things
would be kept as it had been before the Cadiz Constitution. Thus,
Iturbide and the junta declared that they would not be bound by the
Cadiz Constitution but kept the Congress that was convened. That
led to division, which came to a head in February 1822. In its
inauguration, Congress swore that it would never abide for all of the
powers of the state to fall into the hands of a single person or
entity. It, however, proceeded to assign sovereignty to itself, rather
than to the people, and proclaimed that it held all three powers of
the State. It also considered lowering military pay and decreasing the
size of the army. Those moves threatened to reduce Iturbide's
influence in current and future governments.
Iturbide assumed the role of Emperor a month later, and dissolved this congress in October:
Iturbide closed down the Congress on 31 October 1822 and created a new
junta, the National Institutional Junta, to legislate in its place two
days later, answering only to himself.