I'm not sure I completely follow where your alarm panel is and how the existing wire is run from the attic down to there.
Is the panel in the basement under the stairs? Does the wire from the attic drop down into the wall that encloses the stairs on the second floor?
Typically, a stairwell is framed with joists on all sides. Since the stairwell opening often doesn't line up with the spacing of regular joists, the joists framing the stairwell are trimmer joists, which may be a double thickness, composed of two boards nailed together (e.g. two 2x10s).
The studs in the wall on the lower level will be capped with a top plate, which is usually composed of two 2x4s. Then, the joists sit on top of the top plate. The subfloor for the next level sits on top of the joists. On top of the subfloor will be the bottom plate for the wall on the next level, composed of a single 2x4, and then the studs for the wall on top of that.
So, from top to bottom, you would see:
Wall studs for second floor wall
Bottom plate of second floor wall (one 2x4)
Subfloor of second floor
Joist
Top Plate of first floor wall (two 2x4s)
Wall studs of first floor wall
So drilling up from below, you would have to drill through the top plate 2x4s, possibly the trimmer joists, the subfloor, and the bottom plate for the upper floor.