(a) After an initial application has been made, notice to an adverse party for each subsequent application shall be made in the same manner as is required for a motion filed in a pending civil action in a district court. This subsection applies only if:
(1) jurisdiction over the adverse party has been established by service of process on the party or in rem for the initial application; and
(2) the subsequent application relates to:
(A) the same arbitration or a prospective arbitration under the same agreement to arbitrate; and
(B) the same controversy or controversies.
(b) If Subsection (a) does not apply, service of process shall be made on the adverse party in the manner provided by § 171.094.