A link to some pictures....

Here is a link that might be useful: stairs vs. floor mismatch

Can it be made to match? Maybe?
Can the people doing it manage to get it right? Don't know.
Will it age the same over several years of exposure and use? LIkely not.

It's not as simple as just opening a can of #244 instead of #243.

I would let this one go. In the pictures, at least, the difference is subtle and doesn't bother me at all. It looks like the flooring was factory-finished, the stairs finished on site. If the processes and materials are not identical, so you shouldn't expect their appearance to be identical. Your contractor might manage to satisfy part of your preference, i.e. make the stairway less reddish, but cause some other problem in the process such as making the stairs noticeably darker. The risks and costs of futzing with this are real, and the potential benefits seem small. Unless the photos are misleading, I'd focus my energies elsewhere.

You cannot tell what the final color is until the final finish coat is applied.

Any adjustment you try at this point without a test piece (same wood, same finish) is likely to end up not matching after the final finish is applied.

The risers appear to be rotary cut veneer.
This takes stain differently than the solid wood of the treads, even if they are the same species of wood.

It is a project all by itself to make things like this match perfectly.