There does not seem to be a consistent definition for primary and secondary flight controls. It depends on the aircraft.
The Airbus A310 FCOM distinguishes between primary and secondary controls as follows:
The primary flight controls ensure flight path control and include:
- pitch control, using:
- the elevators, which are hinged to the Trimmable Horizontal Stabilizer (THS), and
- the Trimmable Horizontal Stabilizer (THS) which provides Pitch Trim.
- roll control, using:
- 1 aileron per wing, and
- the 5 outboard spoilers (Nos. 3 to 7) on each upper wing surface, as roll spoilers.
- yaw control, using a single rudder.
[...] The secondary flight controls are lift and drag augmenting devices and
includes:
- flaps: there are one double slotted inboard flap and on single slotted outboard flap.
- slats: there are three slat sections per wing (inner, center and outer). Associated with the slats a Kruger flap is located on the
leading edge of each wing, inboard of the inner slat section.
- spoilers: there are 7 spoilers (Nos. 1 to 7) on each upper wing surface which are used as speed brakes, roll spoilers or ground
spoilers for lift dumping (all 7 surfaces).
(emphasis mine)
Therefore, spoilers can be counted as primary controls, but only those which are actually used as roll spoilers (asymmetric deployment in the air).
As far as I could find, Airbus does not distinguish between primary and secondary controls in subsequent models.
The Boeing 747 FCOM (-400 and -8 models) defines the primary and secondary controls as follows:
The primary flight controls are elevators, ailerons, and rudders. [...]
Secondary flight controls include a moveable horizontal stabilizer, spoilers, and
leading and trailing edge flaps.
(emphasis mine)
Here, spoilers are clearly excluded from the primary flight controls. Other Boeing FCOMs I found define the primary flight controls in a similar way, but do not go into further details about secondary flight controls.